Existence Exists?

In one of the bookstores mentioned the other night, my friend quoted a famous pseudo-philosopher's position on metaphysics: "Existence Exists" (no points if you know who the pseudo-philosopher is). My friend doesn't agree with this person's broader philosophic view, but claimed you "can't deny" this basic metaphysical statement. Being a bit contrary by nature, I did. Fortunately, the lady at the checkout counter called me up to pay before I had to explain why. I think I was going to go off on some absurd Idealist rant that I don't even agree with, which would have done nothing to help the situation.

Now, my flippant denial of the statement was intended more as a joke than anything, but I said it for a reason: "Existence Exists" doesn't really strike me as a particularly true (or at least well-formed) statement. I was going to give some reason why, but I've just googled it and found that someone else already stated most of my concerns here. I actually think there's something even more fundamentally fishy about "Existence Exists", but after struggling with it for almost two days and re-writing critiques at least ten times, I can't quite explain it. I'm pretty sure it has something to do with Russell's Paradox. Any ideas?