Close, but actually large PE firms call the shots. A small number of them control most tech, that’s why all these companies look like cookie cutter copies of each other.
PE firms do exert massive influence, but they aren't really the day to day business drivers. Even including the board is tenuous. Board members are often out of touch with the business and just rubber stamps - look how well the OpenAI board performed. If you think Sam Altman should have been fired, they failed, and if you think he should not have been fired, they failed.