China is for all intents and purposes capitalist; the only thing communist about it is that the ruling party has the word in their name, and that the country is still named a "people's republic". Capitalist property relations were restored by Xiaoping and his supporters in the 70's, and ever since those floodgates were opened the private sector has been growing at a record rate.
The share of state-owned enterprises (SOEs) and state-invested enterprises (SIEs) in the national industrial value-added, which was as high as 72 per cent in 1998, came down to 47.8 per cent in 2003 and further to 45 per cent in 2005. The share of pure private domestic and foreign enterprises (not including collectively-owned ones) was about 50 per cent in 2003. In the marketplaces, the controlled economy now accounts for only 3 per cent of the retail market, down from about 98 per cent in 1978.
-Bhaumik, T.K. Old China's New Economy: The Conquest By A Billion Paupers, p.117
Keep in mind that these numbers stop at 2005; since then there has been even further privatisation.
It should also be noted that the SOEs are mostly located in the primary sector, and in particular industries that are crucial to the country (natural resources is a big one, for example). The primary sector has also recently been steadily declining since the 80's (in terms of % share of GDP), with the tertiary sector increasing at pretty much the same rate. This is, of course, due to the massive inflow of foreign capital and the transformation of China into "the world's workshop".
SOEs are also run basically in the same way as private enterprises, with the only real difference being their source of capital investment. I unfortunately do not currently have much information on this right now, though, but this is unnecessary, as it is a secondary point. I think the claim that "China's economy is all state run" has been completely disproven.
There is absolutely no evidence that the National Bureau of statistics is fabricating their GDP. In fact, what has been reported since the reform of the Xiaoping era actually supports the fact that these numbers are accurate. For example, it would make no sense for them to report the massive fluctuations in GDP that were reported from about 1985 to 1992, and would have made much more sense for them to report steadier numbers. This alone tells me that they are on the whole accurate.
Economies don't have "virtues." Moreover, the fact that you see these issues in "third world" countries that are capitalist (China included, as proven above) disproves your claim.