Your co-worker is silly...you are right. Falling into true "starvation mode" or "panic mode" is a long term thing, but the protein zealots -- a group in which I am a proud card-carrying member

-- are giving you good advice. One big day of exercise is not going to derail your weight loss program -- although you might see a little water weight gain in those sore/well worked muscles for a few days -- however, if you don't feed it while you do that much exercise, your body will eat its lean muscle mass...ick.
Anyway, sorry your "buddy" isn't working out so well. My husband and I have been doing the weight loss thing together. He is a big guy, so he carries weight very well, but he has also taken off 40-some pounds. We are always very careful, though, to be supportive of each other and not NAG or act like the food equivalent of hall monitors. Each person's weight loss journey is their own...