This explanation gives an incomplete view of US/Taiwan/China relations.
US policy is one of "deliberate ambiguity"[1].
As the quote above says:
> we do not support Taiwan independence; and we expect cross-Strait differences to be resolved by peaceful means.
An uniformed reader might take that to mean that the US doesn't support the Taiwanese government.
An informed reader realizes what it is saying is that the US does not expect the Taiwanese government to give up a claim to be the government of mainland China. Obviously this is quite a different interpretation, and what "deliberate ambiguity" means.
To quote the Wikipedia article above:
> There is deliberate ambiguity regarding the government of the country of 'China' (as well as what land this country constitutes). Currently, two governments claim legitimate rule and sovereignty over all of China, which they claim includes Mainland China, Hong Kong, Macau and Taiwan, as well as some other islands.
The "six assurances" noted in the comment above also include this "deliberate ambiguity":
> 5: The United States would not alter its position about the sovereignty of Taiwan which was, that the question was one to be decided peacefully by the Chinese themselves, and would not pressure Taiwan to enter into negotiations with China
> 6. The United States would not formally recognize Chinese sovereignty over Taiwan.
[1] https://en.wikipedia.org/wiki/Policy_of_deliberate_ambiguity