One last time, then.
What the Germans were doing was part of Imperial politics, as was the British response.
The Germans offered assistance (veiled or otherwise) to a nation in conflict (diplomatic, economic or military) with Britain. This was considered an act hostile to Britain, by the British.
Was the British response high handed? Undoubtably. Was it unprecedented within the diplomatic norms of the era? Not at all. Bismarck had manipulated this 'high handed' nature of diplomatic relations to his (and Germany's) advantage with the Ems Dispatch in 1870.
My point is that the German actions were antagonist to the British, with their self-avowed 'primacy' in South Africa. This itself was completely fine in the context of the times, just not an action to gain an alliance or benevolent neutrality from the British. The same goes even further for the HSF.
Not "right" or "wrong" just not the best course of action to keep the British out of the entente orbit.
The text actually shows the Germans congratulating the Boers for fending off an invasion by nonaligned freebooters. There is no offer of assistance (see, here's how an offer for assistance sounds: "Next time you need help repelling freebooters who are
clearly not acting on behalf of the British government, let us know so we can help")
The British considered it a hostile act because they did indeed intend to forcibly annex the Transvaal without any concession or consideration of legitimate German interests there, and they considered it repugnant that the Germans would even dare standing up for rights that the British took for granted for themselves.
If Britain actually cared about having a non-hostile Germany, they would have played ball behind closed doors, offering concessions in exchange for a free hand, as they did with the French. Had they done this, it is far less likely that Germany would have even felt the need to build up the HSF. Instead, they insisted (as some folks do even today) that Germany just needed to follow an inoffensive course, with "inoffensive" being defined as "accepting British hegemony in all your foreign dealings".
Hey, Britain wasn't the first or only hegemon to play hardball, so no demonization implied; but why not be honest about it?
Anyway, to tie this back into the OP, if we want Germany to build fewer dreadnoughts, one thing we need is for Britain to accept her into the Good Old Boy club as she had with France. By making back-room deals with Germany, giving concessions in exchange for noninterference, this probably could have been achieved. But since the British obviously weren't interested in doing this, we're set up for
some form of Anglo-German hostility, whether it takes the shape of battleships or not, regardless of other circumstances.