YC is a private corporation, they can fund anyone they want. It's not like a public office.
The mistake you're making is similar to the one where right-wing conspiracy theorists argue that getting censored by Twitter is a First Amendment violation. It isn't because Twitter is not part of the government.
Not saying you're wrong about this specific case, but I don't think the term "conflict of interest" is exclusive to the government. For (a somewhat vague) example, if I recommended my friend to a position at the company I worked for, "conflict of interest" would be an accurate descriptor for me being the one who interviews him for the position.
The mistake you're making is similar to the one where right-wing conspiracy theorists argue that getting censored by Twitter is a First Amendment violation. It isn't because Twitter is not part of the government.