Fomenko? That conspiracy theorist isn't worth the time of day. Yes, Paul pulled out of India but by the time he was doing that the Marathas were doing his job for him.
To deny Fomenko authority within DBWI framework is something close to a sacrilege (*)
Well, let's separate DBWI legend from the DBWI facts. Sorry for a long-windiness.
There were 2 completely separate things.
The 1st one, usually (and quite mistakenly) referenced as "
Paul's expedition to India" was a knee jerk reaction to a combination of a failed assassination and Nelson's excessive eagerness (he was openly bragging about his plans to cut down the "trunk",Paul, of the Neutrality League "tree" in which Sweden and Denmark had been just branches). While nobody denies the obvious fact that Nelson was a great naval tactician, his mental capacities in other areas were not always quite adequate (like asking the government to take care of Emma and his daughter). Surely, appearance of his squadron in the vicinity of Kronstadt was quite untimely (even if there is no indication that he was aware of the assassination plot) and request to let his squadron into the port "for resupplies" was considered as an extreme arrogance. All of the above added to Paul's earlier irritation over the issues of Malta and maltreatment of the Russian contingent involved in the British-Russian attempt to land in Holland. Of course, he freaked out and decided to do something "visible" ASAP. The most obvious (and the most foolish) action would be to order a contingent of the Cossacks of Don to start riding "toward India". This "expedition" was widely advertised in expectation (not quite unfounded) that the Brits would be reacting by sending reinforcements to the Company troops in India (even in Russia very few people knew the details of that "expedition" so the rumors were about a huge host of the Cossacks and irregular nomads, Kalmuks and Bashkirs, riding to India). Taking into an account that even in the relatively late XIX the British government had very vague idea about geography of the space between (what became by that time) Russian Empire and India in the terms of the distances, landscape and local population, it should come as not a big surprise that the bite was swallowed and, instead of strengthening the Caribbean, the troops had been sent to India. In a meantime Paul ordered to arrest all British merchant ships in the Russian ports (something like two hundreds, IIRC) and to confiscate all British goods and properties in Russia: with a hype about India, this action got a little attention.
2nd,
reality. Soon after the 1st order had been issues there was a sobering up. While Paul (and Russians in general) also did not have an adequate knowledge of Afghanistan, Pamirs and other relevant details, the problems related to crossing even more or less known areas of the Turkestan (including Khiva and Bukhara) were generally recognized. It was obvious that no troops would not be able to march across couple thousand miles of a mostly hostile territory with the vast deserts and rather high mountains. OTOH, it was obvious that the Marathas could benefit from the current European expertise. They did have a lot of Sepoy troops trained by the French officers and the Brits reported that their artillery was quite good in the terms of material. However, experience of their French commanders was quite dated and the same goes for their leader, Pierre Perrone (sp) who was not eager to fight against the Brits to start with (**). The Sepoys had been trained mostly along the lines of a typical XVIII century infantry tactics with its heavy reliance on fire vs. the bayonet charge. The same goes for the artillery. While the guns had been quite good, the artillery could not maneuver on a battlefield and commanders had no idea about concentration of fire, horse artillery, etc.
It was decided to send
in secret few experts with a much modern experience. Candidacy of a leader was more or less obvious: in 1798 Lieutenant colonel Yermolov was fired from the service and sent to Kostroma at the suspicion of being politically unreliable. Prior to that he distinguished himself during the Polish campaign of 1794 (under command of Suvorov), war of the 1st coalition (in Austrian army) and in the Perisan campaign of 1796. He already had a solid reputation of a very good artillery commander and extremely brave and energetic officer (had been awarded St. George of the 4th class and St. Vladimir of the 4th class). He kept professing his loyalty to Paul and was eager to take any assignment. For the infantry tactics, search for the cadres was even easier: there were plenty of junior officers and non-comms, fresh from Suvorov's campaigns in Italy and Alps and well versed in the aggressive tactics that was heavily relying upon the bayonet charges (as one of Paul's confidants, Count Arakcheev put it, "if the Austrians could learn how to fight Suvorov's way, anybody can"). So the small expedition of the future instructors had been quietly assembled and strengthened by few French officers secretly sent to Russia. They managed to travel through Persia (at peace with Russia at that time) and safely reached Marathas territory where they spent the next couple years training the local troops. The Second Anglo-Maratha War of 1803 - 06 ended as a draw with neither side making any serious territorial gains. Strategically, the Brits failed to secure Deccan Plateu and officially repudiated Treaty of Bassein. OTOH, with an exception of the tiny territory of Surat, Marathas failed to squeeze
British East India Company from the territories it already controlled.
By a number of not quite clear political considerations (secret letters exchanged between Paul and Napoleon on that subject never had been found) the true "expedition" was kept secret while the fake Cossack "march on India" had been over-advertised thus paving the way to the numerous legends on both sides: for a while the Brits seriously believed in the Cossacks as a potential invasion force while the Russians of a "patriotic persuasion" had been engaging in all types of the fantasies all the way to the "Cossacks defeating Brits in India" (which had been routinely confusing the British government with the British East India Company and even declaring that by 1800 the whole India was British colony).
As I already mentioned, the whole period of the late XVIII - early XIX was a subject of the dedicated political propaganda with the resulting historic legends that had little contact with the reality but served to ...er... "lifting national spirit" (***)
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(*)
Outside of DBWI universe, he is not just a "conspiracy theorist" but a complete lunatic (ditto for his co-writers). His ideas about the Russian world-wide preeminence (based mostly on the facts that name "Vladimir" means "ruler of the world" and that river Don exists both in Russia and in England) would be funny if they were not backed by a
fundamental ignorance (in history, general culture, archeology, etc.) and application of the pseudo-scientific methods (AFAIK, he is a renowned mathematician). But even then his "true identities" stuff is hysterically funny.
(**) At least in OTL. When he eventually returned to France Napoleon treated him quite coldly.
(***) One of the most popular (world-wide) legends was a successful construction of Suez Canal at the order of Napoleon during his Egyptian Campaign with a following transfer of the French flotilla to the Red Sea and planned naval expedition to India which was cancelled due to the diseases in the French force. As (hopefully) everybody knows by now, after the indecisive naval battle at Abukir Bay most of the French fleet had been recalled back to France for support of never materialized attempt to land on the British soil (and idea which Napoleon always considered to be logistically absurd). Suez Canal was constructed few decades later during the reign of Napoleon II, son of Napoleon I nicknamed "Little Napoleon", when the "age of steam" made it practical. It was, indeed, used by the French-Russian expeditions of the mid-XIX for establishing the trade bases on the coast of the subcontinent (the Brits still controlled the East coast, even if with some losses to the expanding Maratha state.
Another, less popular world-wide, legend is related to the alleged Russian help to the American Revolution. The legend is based on 2 seeming unrelated facts: (1) refusal of Catherine II to send help to the Brits against the rebelling colonists and (2) Pugachev rebellion of 1762 - 69. Adherents of this theory are claiming that in 1769 Catherine II made a secret pact with the rebels leadership allowing them to escape to the East all the way to the North America, crossing Bering Strait during the winter, and picking up the Polish "rebels" cooling their heads in Siberia. Allegedly, that host of the Cossacks, Bashkirs and Poles made it all the way to the rebellious colonies (geography never was a problem for the national legends) and arrived by the early 1770's to their destination helping the rebels to win a war. (Presumably) scientific research of the legend can be found in the book "Three headed Eagle".