> $100 million CEO is worth $50 million more than a $50 million CEO, so your economic outcome is the same regardless of which one you hire

What you're suggesting here is not that there's no correlation, but that there is a latent correlation hidden by the market. Another scenario is that some CEOs do well for their companies and some do poorly and this doesn't depend on how well they're paid. In other words, I'd vote for possibility 2, except instead of saying CEO pay and company performance are totally random, I'd say they're independent of each other.