What China shows (and what counters the US rhetoric) is that evidently economic freedom can (at least to some extend) cause prosperity without political freedom. Common wisdom has predicted the rise of some kind of political freedom in China for years now, but what has actually been seen to be on the rise is better governance - an oft-cited example is the case of Bo Xilai[1].
We certainly haven't seen the endgame of China's development. Confidently claiming that China has 'prosperity without political freedom' is simply playing fast and loose with terminology. The stronger and more educated the middle class gets, the more freedoms they demand.
Taiwan and South Korea were dictatorships but get freer every year. Still it took decades of small steps to get where they are today (legitimate elections, opposition parties winning) and clearly China has a long road to even get to where those neighbors are today.
"some kind of political freedom"
While 2013 China is no poster boy for freedom hasn't the situation improved every decade for 40 years? Isn't China today far more permissive and free than in the past? Obviously in terms of elections maybe not so much but looking only at elections might be ignoring real gains made in rule of law, property rights, speech and social freedoms.
The issue is causation. The American mantra for the last 50 years has been that freedom causes economic development. What we're seeing with China is economic prosperity causing increased pressure for political freedom (though at a dramatically slower rate than I think Americans circa 1960 would have predicted).
1: https://en.wikipedia.org/wiki/Bo_Xilai#Downfall