Never worried about it too much but might if I lived somewhere where could be dangerous. I would think it would require sustained proofing to get a hungry dog not to eat food from the floor in every circumstance. Them ignoring it in a "leave it" or "it's your choice" situation is easy - out running about in the park free as lot harder and I think tossed treats in training would not make much difference either way. Tossed treats can be handy for some exercises to reset the dog or as a distraction and doubt doing it influences the chances them eating a discarded burger in the park.

@Nick Benger Sometimes. Other times the demo dog is too polished to get much more than a finished product view which is fine but can be over used. For a beginner/puppy class it does give the instructor some credibility but time doing a demo with a green dog can be more useful.