I read it as "Bill Murray is ugly but doesn't realize that he's not like everyone else" (who presumably are not ugly).
I also read it as a comment from someone unable to be self-critical. When Bill Murray says we're uglier than we think, I assume he doesn't mean that we're all secretly terrible people, but that our flaws are worse than we want to admit to ourselves, that honest introspection hurts because it means confronting those flaws we spent so much time downplaying and ignoring. I'm sure Bill Murray's flaws are not the same as mine or anyone else's, but I'm pretty sure most people have flaws they are unhappy about.
