The problem seems to be that they are asked - and often answer - questions on topics unrelated to that topic, in the belief they're just, y'know, really smart.
I think the economics prize must be the worst banana skin for the recipients - popular economics science books like Freakonomics have cemented in the public's (and journalists'), minds, that economics has applicability to a number of different parts of life. And it does! However that does not mean they have any authority to speak on anything outside of their published work.
We probably shouldn't be treating Nobel prize winners as the smartest people generally, just specifically in the field of their discovery. Very common fallacy to fall for though, and when everyone treats you like a general genius, of course you're going to give your opinions.
I wouldn't go that far. They are not dumb and they like to promote their ideas. They can probably give an above-average take on most things.
There are millions of other not-dumb people who will give their opinions on anything. If you ask them their opinions on everything a lot of them will say crazy stuff, but a Nobel laureate says it it makes more headlines.