When I apply a triangle I usually try to hook the guy's leg with my arm on the same side that my leg is against his neck, to secure a good choking angle. Although we don't slam each other in class, I think that grip also makes it pretty hard to do that. However, grabbing his leg in that way leaves your face open for strikes from his free arm, especially if you're using your other hand to adjust your legs of pull down his head. Although someone who doesn't know how to defend a triangle won't have many seconds to do so.
No offense, but I find it a bit unbelievable that someone who has been training bjj for 2 years would still think a triangle will put you in a position where your opponent can bite your balls.