These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The director states in the commentary that it was intentionally left so that it works whether or not he and JFK are really who they think they are. He specifically points out one line that could be Elvis and JFK talking about their family lives, or both admitting they are fooling themselves.
There's also a moment that implies JFK's story is true, and this makes the other characters' stories more plausible by extension.