Whether he should have said it on moral grounds is one question, and whether it is indicative of handling part of the CEO's job very poorly is another. The CEO is the public face of a company - that is literally part of the job. He did this abysmally, and in many, many companies, it would be enough for a board to sack him. The CEO doesn't get a firewall between their personal life and work, or a pass for off work behaviour. They get paid to live it.

I work in diligence on medium stage companies and the acquirer wondering if they have to ditch some of the current exectutive is very common. (I know nothing about the ownership of YC mind you.)