The thing that jumps to mind is the Security Council, which they can parley into diplomatic favours from other people. And the whole point of the UN is that it was the victors of WWII explaining to the rest of the world how international affairs were going to work, so I'd be pleasantly surprised if the special privileges stopped there.

And even without that, the UN isn't really set up to handle technical matters. It is a diplomatic club. The point is to give people a seat at the table without considering their competence.

Perhaps they mean that Russia, a corrupted warmonger weak country, has veto power, while more powerful, free and democratic countries have not.