The "fanbase" is made of people who have been fans of the developer since before the release of a game. They are conservative about what they like in the developer's games and they are forgiving of flaws, compared to the target audience as a whole. So they will focus on the wrong things in testing, compared to professionals. Is there any evidence that amateur testers know better than professionals about what makes a "good game", or that either kind of tester actually contributed to game design (not testing) in a way that made the difference between a good and a bad game?
What kind of evidence you want? Reports? Books written on the subject? Of course there is no evidence.
Nevertheless...
I'm not sure what do you understand by pro testing, but naggy explained fairly well, what they do. They are paid for debugging and optimization, not about finding good game mechanics, making it fit the target audience and such. Yesterday they have tested racing game, today they test Vicky 2, tomorrow - they will test pinball. They don't analize if strategy game is good, they only test if the interfaces click, if it does what manual says (in clicking terms, menu positioning and such), if game does not CTD and such.
Fan, on the other hand, is a guy that might not be IT specialist, but he is a guy that is supposed to buy the game, and got some sort of vision what such game should achieve. For pro tester, that vision is no bugs. For fan, this vision is that country X will do this, and country Y will do that, leading to something that will make him happy, because it's historical/playsible, whatever.
He can also contribute. Check the AI/event files for HoI2 and names of authors. Check scenarios data. And there was much more - that would be made in much poorer manner, if not fanbase contribution in the beta phase. If you want a proof of improving game by the fanbase, this is the closes thing I can present you.
For me, classic example (even though it seems there was no pro testing team there) of such "working well, but not so good" game is EU:Rome. It's almost absolutely bug free (compared to the other Paradox titles on the lauch day). At the same time, it was huge dissapointment to the fanbase. It might appealed to the new players, its possible. But it was one of the things that alienated the old fanbase and made people more inclined to believe that Paradox games should be bought only, when they reach bargain bin prices.
Combination of pro and fanbase testing is neccessary to keep right balance between game "working" and "being good", that's all.