When we hear that a company has been hacked by China what is usually meant is that the company has been hacked from a computer with a Chinese IP address. The immediate implication is that it is Chinese government sponsored.
Of course, there are many ways in which the attacks might not be from anyone in China at all. Using proxies or compromised computers as relays, would allow the attacker to be anywhere in the world while appearing to be in China. The fact that there is so much hype about Chinese government hacking right now, makes China the perfect false flag for any attacker. It sends investigators down the wrong path immediately. However, there is growing evidence that many of the attacks are actually being perpetrated by independent Chinese civilian criminal hackers out to make a buck. They are intent on stealing and selling intellectual property. The huge supply, and under employment, of computer trained people in China may be to blame. They have the skills, the time, and a need for money.
The Chinese government has also been very lax about trying to track down these individuals and generally suppress this kind of activity. The hacking activity is certainly beneficial to the Chinese economy, as the IP is generally stolen from outside China and sold to give advantage to Chinese companies. That gives a kind of covert and subtle support to the hacking activity without any actual material help or direction.
So, it is not quite government sponsored, and it IS actually Chinese. The bottom line is that it is a real problem, and a threat that is actually harder to track down and prevent because it is so amorphous.