Or, if the President uses his powers to assassinate a governor -- again, explicitly not an official act, as the president has no authority over state elections.

If anyone bothered to read the constitution, it clearly lays out the sorts of things that could be construed as official, and the sorts of things that are not. The President does not have unlimited authority. His scope of authority is rather small, even if several important things fall under it. Part of the problem is the pervasive idea in American electoral politics that the president has some sort of power to 'promise' various laws and such. It's so silly since no President can possibly do that.