Nonetheless, de facto, they are independent. And if you'd glance back at my comment, I deliberately referred to it as "assimilating with mainland China" to pay lip service to them seeing themselves as the true government of China, in an attempt to avoid this very nitpick.
Controversy doesn't change the reality. Stating that Taiwan is not independent is political posturing. Look to French Guiana, which is not independent.
Taipei only disagrees because they're under threat. Doublespeak should generally be called out. Taiwan lives under perpetual fear of occupation and forced assimilation.