Very frequently, yes, they actually do. This especially happens when one guy starts losing the stand-up fight and starts getting his face beaten in. It's natural. Clinches happen all the time when one fighter (or both) get tired. It's dirt common in Boxing. Takedown-to-groundfight is also a lot more common now than many realize because of the influence of MMA.
Sorry, but, now. He's not wrong, it does happen with regularity. All the time? Obviously not. 90% of the time? Not likely. 10% of the time? Also not likely. How often? Hard to say:
http://cbd.atspace.com/articles/90percentmyth/90percentmyth.html
Peace favor your sword,
Kirk