To figure out a strange plot, look at what happens, then ask who benefits. Except that Dumbledore didn't plan on you trying to save Granger at her trial, he tried to stop you from doing that. What would've happened if Granger had gone to Azkaban? House Malfoy and House Potter would've hated each other forever. Of all the suspects, the only one who wants that is Dumbledore. So it fits. It all fits. The one who really committed the murder is - Albus Dumbledore!

I think if you use this line of reasoning and then allow yourself to dismiss arbitrary parts of it as "not part of the plan", you can make a convincing argument for almost anything. For that reason, I consider the entire theory suspect.