I don't recall ever seeing Misty ref, and I know we've never seen Ash ref (although that sounds like it would be kinda interesting). Think back to Ash fighting Price and there was a direct mention that they could not battle without a ref, and then that lady (I forget her name) turned out to be an official ref. And I think they called it a referee too, so at least in the English dub, that's the title.
I bet that it's an alluring profession. By being a ref you get to see up close and personal some awsome battles, and meet lots of friends and see lots of Pokemon. I'm sure that you need to know advanced rules and ways of telling whether a Pokemon is out or about to get back up. Refs can also disqualify someone for breaking the rules, such as when their Pokemon leaves the battlefield, or when it refuses to battle, etc.
Always remember that Brock is the eldest of the bunch, and besides being a Gym Leader and aspiring Breeder (a rare and complex profession. How many breeders have we seen? How many times has Brock said a little tidbit about Pokemon that a Professor found interesting? Being a breeder is neither common place nor easy). Brock is also hella smart. I wouldn't be at all surprised if he held an official "ref" title, or some form of official certification.
The worst ref we ever saw was the ref for the match between Blaziken and Charizard. That ref ruled Blaziken unable to battle, and then allowed the match to continue when Blaziken got back up. WHatever! Pikachu was up and clapping his paws and cheering mere minutes after being knocked out, so why couldn't he battle after being ruled out? The answer: That ref made a bad decision to allow the match to continue and Ash should have challenged. Blaziken was down and out and had the ref not stepped in, then Ash could have had Charizard finish it off while it was down.