Well... sort of? The short answer is yes, of course they are. But I don't think they quite view themselves as the same as other US citizens exactly. Both US and Puerto Rican courts have repeatedly recognized Puerto Rican citizenship as distinct from US Citizenship, as does the EU. Spain, for an example, allows Puerto Rican citizens to become Spanish citizens after living in Spain only two years (as opposed to ten years for other US citizens). The CIA World Fact Book defines the people of Puerto Rico as "Puerto Rican (US Citizenship)", as opposed to the entry for the US which defines the people as "American".
Considering that statehood movements in Puerto Rico have historically been dismal, I suspect they like to be straddling the line of being "American".
I'm not sure who would find financial or other benefit from acquiring Puerto Rico from the US, and independence votes there have been even more unpopular than statehood votes. So I don't think they'll be separating from the US any time soon. But after much rhetoric from Trump and other Republican politicians, I'm sure there are plenty of right wing folks that would delight in seeing them go.
Edit: Puerto Rico Act 22[1] is the law in question.
Self-determination is important, and selling land with an entire culture and population based solely on a balance sheet seems shameful. That said, if the deal were mutually beneficial for Puerto Rico and the US (“We’ll invest heavily enough in PR to make them interested in approving the deal in a public referendum”) that would be fine.
Puerto Ricans seem split of statehood, but full independence seems far less popular, at least based on the 2012 referendum.
I'd like them to become a US state. I feel similarly about all territories under US control. I feel it would be ultimately better for them than independence, and better for US moral character.
If they want out I'm sure they could have out.
They really aren't treated as such, particularly of late. I doubt many would be against it, though this is 100% an outside perspective and I agree with others that it should be self determination via vote if it was ever to occur.