The adage is true, but when you think of things that you remember fondly from your own memories of pro wrestling, aren't the funny things the ones that stick out in your mind?
The problem is that a lot of what wrestling offers as funny isn't funny. That's why we have moments where Triple H rigorously copulated with a mannequin named Katie Vick or Vince McMahon laughed maniacally over a penis pump he received as a gift that blew up in his face. Again, a lot of it is this "audience of one" problem that WWE has. TNA is guilty--remember how Kevin Nash buried the X-Division and made-believe he was some kind of therapist? And don't get me started on the indy show I went to where they had a "dildo on a pole" match.
The adage should really state: "funny doesn't draw money when it's not funny". There's no doubt that Rock, Austin and the stars of the Attitude era and the New World Order could back up their mic skills in the ring. But if Rock was on a show and the fans didn't get to sing along with a champ, you just KNOW there would be a riot.
The nice thing about today's crop of "funny" stars is that the humor is more natural and not as forced. Guys can be funny without cutting promos. Social media allows for more flexibility. This is why we've seen guys like Zack Ryder and Colt Cabana draw a fan base outside of the traditional WWE marketing machine.
So, yeah... funny does draw money, and it has throughout history:
Eddie & Chavo Guerrero
Steve Austin and Kurt Angle:
Edge and Christian:
Rowdy Roddy Piper: