I don't have enough data to prove or disprove this statement - although I do know a lot of working and non-working artists, and anecdotally skill seems to win out.

I'd agree, if you're intending to be an A-list star and won't settle for anything less, luck is going to have to play a pretty significant role. But there are a lot of jobs and opportunities for an actor, for example, outside the "best of the best" situation.

I was mostly replying in support of the comment above from randomdrake, however.