So the US didn't officially support "Taiwan independence". After the US flipped to PRC, they opposed the PRC taking over Taiwan, but the "Taiwan independence" notion didn't exist in Taiwan at the time. The govt in Taiwan wanted to retake the mainland. The independence notion only came into existance relatively recently.
ie. The original generation that considered themselves Chinese has mostly died off, and now the younger generation who consider themselves Taiwanese are slowly taking over.
In reality, the US doesn't believe that they're the same country: the status quo is that they aren't. The fact that the US can't say as much out loud, to avoid insulting the government of the PRC, doesn't make that any less true.
I guess what I'm saying is, nobody should pretend that the the official pronouncements of the US are its actual beliefs or policy around Taiwan. Everybody knows the US supports Taiwan staying independent, and just has to dance around that in public statements. Anything it says to the contrary is a polite fiction without real world effect.
If by that you mean the US agreed that Taiwan should be a part of the PRC, that's never been true. It was just a condition of establishing relations with China that the US officially pretend that Taiwan isn't an independent nation. But everyone understood that the actual belief and policy of the US was that Taiwan has a right to independence. There hasn't been any change there.