How could Taiwan have become American territory (most likely some sort of Commonwealth a la Philippines and the other Spanish-American War acquired territories, as opposed to an actual state)?
1. I think it would require a drastic change to American policy towards China, which was rather moderate as opposed to the Europeans' actions at the time.
2. It would require the U.S. to actually bother to want to take Taiwan and go through all of the trouble of governing it. Not to mention fight a war over it, or negotiate with the Europeans and the Japanese.
3. It would require the Europeans to allow the U.S. to grab Taiwan.
Anything else?