Does China's government hack US companies to steal secrets?

Yes, of course. So did Russia.

See the movie Farewell, based on actual events? http://www.rottentomatoes.com/m/farewell_2010/

The point being, if they could, and if it helped them, and if there was no real/strong enforcement against it, why wouldn't they have done so? Of course, not the Chinese govt. directly, that would be bad form; but a sponsored organization, I don't see why not, they are ambitious enough.