So I wouldn't really consider citizens of US territories full US citizens.
So maybe it's more appropriate to say they aren't Americans, but they are US citizens.
But that is all semantics. My main point was the reason they don't have US representation is they don't have US taxation.
A Puerto Rican in California is entitled to all the benefits of US Citizenship whereas a Californian in Puerto Rico is not. Mostly these are related to welfare and elections. This would be the case for the Californian or Puerto Rican living anywhere in the world outside the US.
So a Californian that moves to, say, Germany can still vote by mail as though they were in California.
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You're mostly correct about the loss of welfare benefits, though. The only exception being that you do remain eligible for Social Security retirement, although some people may not consider that "welfare".
The District of Columbia has to pay US taxes without being allowed any US representation.