After reading cfircav8r's useful post I'd like to modify my remarks a bit. One reason downwind turns cause problems is that the extra ground speed when flying downwind can cause pilots to think they're flying faster than they really are, and when this happens they are closer to a stall than they think (Post No. 8). Another reason is that if you are flying downwind and then turn, you'll have to turn more sharply than in calm wind to get the same turn (in relation to the ground) than in calm air. circav8r is right that if you use the same control inputs that you'd use when it's calm you wouldn't have a problem. But you're not likely to do that, so, as he says, you'll likely tighten your turn. That means you're pulling more G's and using more up elevator than otherwise, and that in turn makes you more likely to stall.

Furthermore, a lot of RC pilots don't really have a base leg in their landing approach. Instead of flying a rectangular pattern, they just fly downwind and then do a sort of semicircle and come around into the wind. That makes it even harder for them to judge speed and the attitude, as they're looking at the plane from a different angle all the time through the turn, and it means they're pretty much going straight from downwind to upwind all at once, instead of in two stages. Doing it that way also makes it easier to get your angle of attack too high than if you make 90-degree turns and fly a straight base leg. This isn't really a "downwind turn" problem, as it can be a problem even on a calm day. But on a windy day, this happens at the same place you're making the dreaded downwind turn, so the wind may get blamed.

Bottom line: turning too sharp, too slow can get you in trouble. The downwind turn condition and the rounded-off approach can both cause people's turns to be too sharp and too slow.