I think it does deserve eye roll, because it is huge oversimplification on itself. The situations in which you convince people with facts are not exactly rare.
That person is getting an eye roll, because they are just repeating popular phrase that is not even particularly useful.
I was about to say, I've definitely had my mind changed mid-meeting by facts, even if the person trying to convince me was being an asshole. It might not happen as often as it should, but I think it's somewhere between "reductive" and "untrue" to say that you're not going to convince educated people with facts sometimes.
That person is getting an eye roll, because they are just repeating popular phrase that is not even particularly useful.