This is just the normal Chinese gov control everything narrative that people who've basically not spent a lot of time in china tell themselves for whatever reasons.
CCP preserves CCPs power. That's its main focus, it controls what it needs to, to do that. Which it achieves by controlling just the top tier business like 10-20 of them. The other 25,999,980 businesses would likely never hear anything from the CCP in any meaningful way.
This is not dissimilar to how government has fairly significant influence over Amazon/Apple/Facebook etc in the US.
Note: I'm not defending CCP here, they do stupid/bad stuff but controlling every single business is not one of them.