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.
There are a lot of broken things in the US but it does have some modicum of separation between business entities and the government as well as a sort of psuedo attempt at rule of law.
[0] https://www.theguardian.com/world/2019/jul/25/china-business...
There are lots of communist party members in lots of organisations. Just like there are lots of republicans in organisations.
But the premise that you are trying to support is: ccp “controls” all the companies. Not: ccp membership can be found in lots of companies.