Was Teddy telling the truth?

Memento has been the best movie we have seen so far this year in Art of Film (In my opinion). I enjoyed Groundhog Day a lot, however I had already seen that multiple times. Memento is a one of a kind movie, mixed with its reverse chronological order and Leonard's condition, it was so much more than I expected. The whole movie led up to the final scene, which in the black and white scenes case was the ending and the color scenes case, was the beginning. Here we learn how Teddy may not have been lying to Leonard the whole time, he may in fact have been a cop and tried to just help Leonard. We learn how Teddy had Leonard kill a guy to try and get the money out of the trunk and in doing so explained how there was no Sammy Jenkis and Leonard was really the one who couldn't condition his memory to save his wife. These ideas are very interesting, definitely make you think and question your entire viewpoint of the film thus far. My conclusion was the same one that Leonard drew, he burned the pictures of himself after he supposedly killed "John G" and the picture of the man who was supposedly "John G". I think Teddy had been lying the whole time to try and make off with the money and not get caught by Leonard for who he really was, John G. who raped and murdered his wife.