The problem with Nicholas was not a presence or absence or a "reason" (which is a highly subjective thing) but a plain fact that the cornerstone of his foreign policy was principle of "legitimacy" and support of the Hungarian rebellion would go against that principle as Nicholas chose to understand it at the moment.
However, I don't think that scenario is 100% hopeless. All these principles had been nice and fine but they did not prevent Nicholas from supporting the Greek rebellion against the Ottomans or infringing upon the Ottoman sovereignty in the issue of the local Christians. If he was really 100% dedicated to the letter of principle he preached he would also reject legitimacy of Charles XIV of Sweden instead of being quite friendly with him, probably would have problems with letting his daughter to marry Maximilian Joseph Eugene Auguste
Napoleon de Beauharnais, 3rd Duke of Leuchtenberg (yes, no directly compromising blood but, still, linkage to a VERY BAD PERSON was undeniable).
If the Greek rebellion was justifiable, why not the Hungarian one? After all, unlike Greece, Hungary was a clearly defined state that was linked to other Hapsburg possessions just by a personal union. The fact that the Hapsburgs had been using troops of the vassals of Kingdom of Hungary (Bannat, Serbs) against Hungary could be considered as violation of the legitimacy principle (toward Hungary) thus giving more justification to Nicholas actions. Of course, Nesselrode must be sent into a retirement but this is not a noticeable problem.
Well, of course, Nicholas would be pointed (by whom?) to his own Polish Rebellion but who is without a sin and, anyway, these Poles were just a bunch of the ingrates while the noble Magyars are fighting against the evil Hapsburg oppressors; a completely different situation as anyone can see.
Anyway, Franz Joseph was not recognized as "King of Hungary" by the Hungarian parliament, and he was not crowned as "King of Hungary" (until much later in OTL) so this is not even a rebellion against a legitimate monarch and no principles are violated. As far as the Hungarian liberalism is involved, in OTL Hungary was not declared a republic until 1849 and formally still was a constitutional monarchy with a reasonably moderate government led by Count Batthyány (in OTL, AFAIK, his government was not doing anything excessively "revolutionary"). Earlier Russian intervention on the Hungarian side means that more extreme figures, like
Lajos Kossuth (Finance Minister in Batthyány government) are marginalized, at least for a while. After the Hapsburgs are defeated, Hungary remains a constitutional monarchy and some suitable king can be found either among Nicholas' sons or among the countless German princes (like Otto Wittelsbach, Otto I of Greece).
Not sure about the absence of a foreign support either.
Germany: The lofty principles were all nice and good but they did not remove the rivalry between Austria and Prussia (and the notion of the German unification already was in the air even if
Frederick William IV considered it being too revolutionary and feared that the formation of a
German Empire would mean the end of Prussia's independence within the German states). Serious weakening of the Hapsburgs would strengthen Prussian position in Germany so probably not too many objections from that corner.
France: In 1848 had its own
révolution de Février which ended the rule of Orleans dynasty and established 2nd Republic. If anything, Nicholas would be applauded and this attitude would not change after the coup of 1851 because soon enough Nappy #3 was fighting against the Hapsburgs.
Kingdom of Sardinia: In 1848 at war with Austria (which it was losing in OTL) so any enemy of the Hapsburgs is their friend.
Spain: In the midst of the Carlist Wars and it is not like it mattered at that time, anyway.
The Ottoman Empire: In a process of modernization and, keeping in mind general history of its foreign relations, why would they be against independent Hungary? Surely, not because of the excessive obsession with the issue of "legitimacy".
The Brits: May or may not be upset as a matter of a general attitude toward what can be considered as Russian expansionism but can do little without a powerful ally on the continent and the only candidate to such an alliance is just in a process of being beaten by the Russians and Hungarians.
Sweden & Norway: Oscar I is quite liberal (within the reasonable limits) in his principles and owns nothing to the Hapsburgs.
What's left? The Netherlands, Portugal, Denmark, Naples, Switzerland, etc. all the way to Princedom of Monaco. Who cares?