Actually no. Survivorship bias is precisely the act of using self referential anecdotal evidence and extrapolating it beyond its appropriate scope.
He used a self-referential anecdote to conclude something about himself, and nobody else. That is perfectly valid use of an anecdote. Just because anecdotes are often used incorrectly does not mean that every use of an anecdote is incorrect. You just saw an anecdote in a conversation and dutifully recited the logical fallacy lines.
For it to not be survivorship bias the anecdote needs to explore data beyond ones self.
No, it does not. He is not seeking to make any conclusion beyond himself. Why would he need extra data? He is saying "I've never had an accident, therefore given that past performance is a reasonable indicator of future performance, I conclude that I am a good driver." That is a perfectly valid statement. If he tried to conclude anything beyond himself, you might have a case. But, as it stands, he is not, so you don't.
The only thing dumber than a person who makes logical fallacies, is someone calling others out on logical fallacies incorrectly. Stop it, you're embarrassing yourself.