I recently read in a book called Contrary to Popular Belief that George Washington was in fact the thirteenth president of the US. Is there any truth to this?
I suspect that is referring (at least in part) to the pre-Constitution office of President of Congress (aka: President of the United States in Congress Assembled).
The pre-Constitutional governments were a very different kind of government though, and those offices were roughly equivalent to the modern Speaker of the House, not to the modern USA office of President.
The president was a member of Congress elected by the other delegates to serve as an impartial moderator during meetings of Congress. Designed to be a largely ceremonial position without much influence, the office was unrelated to the later office of President of the United States
So I don't think its reasonable, or helpful, to consider it equivalent to the office George Washington held in 1789. I hope the rest of that book's "facts" aren't of similar quality.