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You could reconcile it by believing that people just don’t understand percentages.

The obvious reconciliation is that "they" all live "over there".

This is probably true. I'd also add though, how would most Americans even know if they've met someone who's transgender? By definition, the transition phase is transitory.

We’re talking methodology so I think it’s fair to dig deeper.

The most obvious point is, how do you tell someone you met is transgender ? The question itself is pretty weird IMHO.

It would also be interesting to see how many gay people the Americans responding to the pew survey reported to have met.

All in all, these survey are about what people think, it seems pretty hard to come up with control numbers, or validate a methodology as much better than another in meaningful ways. At most we could have different surveys from different groups converging toward the same numbers.

Perception does not equal reality.