I prefer to think John Gammell was a total liar.
I think when people still call him 'Teddy', they fall victim into believing him.
I prefer to see this as irony, Leonard setting up the death of Teddy because of Jimmy and actually killing the John G.
To me the name John G is not coincidence.
I do not see John Gammell's actions as that of a real police officer (or why a San Francisco cop would be in LA)
I believe he is telling the truth when he says "I'm a snitch"
I don't think any cop would handle the Dodd situation that way.
Nor would they think of trophy hunting Jimmy's shoes, as John Gammell does.
I felt this way before reading Memento Mori, which I feel is most similar to the above interpretation.
This does not mean that Teddy raped and killed Leonard's wife.
The origin and accuracy of Leonard's tattoo is very suspect.
However, if there were drugs in the car, as in Leonard's story, then they probably stole them from Leonard's house.
Leonard seems well-versed in handling a gun during the flashback of the break-in.
Was John G responsible for sending in two guys to rob Leonard?
How can anyone trust that the first revenge killing by Leonard had anything to do with John G if John G set it up?
I know this view is not popular, and some will say it is not supported by the film.
However, it is very telling in the scene where Leonard says you can tell if someone is lying by observing them, not by what they say. And in the end, in the assessment of this film, that is all we really have.
(I do not include any auxiliary information outside of the film itself.)