Capitalists largely govern the medium firms, but systems like the CPC's golden share prevent them from acting willy nilly. Smaller firms are either cooperatives or petty bourgeois. The bourgeoisie does not have political power, because they do not control the commanding heights of industry. The rubber factory has control over the rubber ball factory, as an example.

To a degree, you're correct in hinting at the social safety nets being more comprehensive in the past in China, but at the same time real wages have dramatically increased year over year. China's economy is one filled with contradictions, and is one that has changed dynamically over the years, yet in all that time the proletariat has had control over the state and the bourgeoisie been under its thumb.

ProleWiki has a great page on Socialism with Chinese Characteristics, same with Qiao Collective.

And merry Christmas!