> the "bad" sort of private equity

People mean "acquired by a Private Equity firm". You can learn what one of those is here: https://en.wikipedia.org/wiki/Private_equity_firm

Yeah people generally mean PE investment firms that are in the business of moving around and sucking up companies for short terms and stripping them to squeeze all the money out and then moving on to the next one. Not simply that a company’s equity is privately held, not publicly traded.