> Is that how that generally works, or am I making uninformed assumptions?
The answer is probably a bit more nuanced, but broadly, you're making uninformed assumptions. Blackrock own about 5% of Apple, Nvidia, Microsoft, and we don't see people throwing around accusations that they're fiddling with their runnings.
I used to work for a company that Tencent had a minority (but significantly larger than 9%) share in, and they approximately 0 influence in our operations. Some places will be different, but if you've ever worked anywhere with a parent company you'll be familiar with just how untrusting the subisidiaries are. Honestly, I think the best way of thinking about it is the Larry Ellison Lawnmower joke - they're not out to get you, they don't care.
Whether or not that remains to be true going forwards who knows, but that's the same of any organisation anywhere in the world, and as someone who lives in Europe I'm far more concerned about what the US is doing right now.