I think there is an element that the "He was holding a referendum, which means that it was democratic" side of things are missing ...
In most democratic governments a law must be passed by the legislative branch and approved by the judicial and/or executive branch of the government before any legally binding referendum can be held. On top of this, in many countries there are laws on the books which state how the country's constitution can be modified, and in many cases it is not something that can be done through a referendum. I'm not informed enough about the situation in Honduras but (from the sound of it) Zelaya did not have the legal right to hold a referendum to modify the constitution and he decided to hold one anyways.
Without even considering whether or not Zelaya was trying to get foreign powers to influence an election (he couldn't win otherwise) to favour him, the fact that Zelaya was trying to hold an illegal referendum was probably justification enough to have him removed as the president of the country.
