Blackrock does not at all operate the same as a private equity and it's a huge pet peeve of mine when people lump them in together. Usually they are confusing Blackrock with Blackstone.
All Blackrock does is manage wealth and investments on behalf of individual clients. One of the ways they do this is by sticking private assets into funds for their clients. It's more akin to Vanguard than anything to do with private equity. There's no reason to believe BlackRock would be breathing down their necks when all they do is broker the funds on behalf of their clients.
Automattic DOES have private equity backers though like Tiger Global, Insight, ICONIQ, and more.