Remember, we're talking about Google introducing fact checking. In this context, "fact checking is not enough" is a very different position from "fact checking is subjective".

> Remember, we're talking about Google introducing fact checking

Exactly. And he is saying that even if Google's fact checking works, it still doesn't equate to the piece begin unbiased or truth,

Even more simply said again: You can lie with the true.

Fact checking isn't subjective, though. You either do fact-checking or you don't. If you do fact-checking, you're either checking if the statement is factually correct or not. There is no real in-between and no real "this is true because I think it is."

At least from a human perspective. You're right in raising the concern that from a machine perspective this is hard to achieve, but again that's a red herring to the OP.