Yikes!
I never eat while interpreting. I only bring a bottle of water. If I am hungry between assignments, I bring a yogurt fruit smoothie in a cooler in my car. I just drink that for quick nutrition. If someone offers me food, I just smile and say, "Thank you, but I don't eat while I am on duty."
Too many risks of eating while interpreting, like in your example. Also, suppose the terp starts choking, or spills a soda, or has a lovely bit of food stuck between the front teeth? Ha, ha, better safe than sorry!