Sentence 1. is indeed ambiguous in terms of its intended meaning.
"position" can mean
a) a point of view adopted and held to.
If the US "acknowledges the position that..." then it accepts that there are some people who believe it.
If they "acknowledge that..." then they accept the truth of the statement.
"position" can also mean
b) the point or area occupied by a physical object
c) relative place, situation, or standing
"The US acknowledges Taiwan's position in China" could mean that Taiwan is situated inside of China, but could also be referring to Taiwan's political standing in regards to China. For an unambiguously geographical meaning, the whole sentence (and the Earth) would have to be restructured.
To mean acknowledging the truth of Taiwan "belonging" to China, this should be:
The US acknowledges Taiwan's position as part of China.
The US acknowledges the position that Taiwan has as part of China.
which is definition c).
So what sentence 1 really means is that the US acknowledges others' opinions about Taiwan being part of China. Whether this is what is really meant, or whether "position" was accidentally misused, or whether it was used to pretend a meaning that isn't there, by association with other definitions (doublespeak), is anyone's guess.