But I also have some specific reasoning that leads me to believe it's not a poor choice to provide another way to sign in. Signing in with facebook is extremely easy compared to normal signup paths. What this means is that most people who trust you with facebook will still sign in via facebook. And I don't think there's much of an argument that people who don't trust you with facebook will be signing in with facebook if it's the only option.
You can always allow them to link with facebook later, after they know what the game is, and after you've explained to them why linking will be valuable to them.
You're assuming that more options always increases value, but this is not the case. See Apple and, let's say, the Samsung Jitterbug for counter-examples.
However the claim I was debating was that a second sign-in method would be bad because people would exercise it. The argument was basically that it's bad because it's increasing value for users in a way that decreases value for you. And I don't think adding a second sign-in method to a page that currently only has one button really causes a difficult or confusing decision or creates a cluttered UI.
I suppose I still do see your point, though, since I personally wouldn't go much beyond that -- "sign in with facebook or twitter or google or browserid or github or create an account or or or" sounds like a miserable experience.