Answer:
True
Explanation:
Having an shoe that does not match the exercise will only serve to hinder you. Imagine doing ballet in heels, soccer in ballet shoes, swimming with boots, etc. Having adequate shoes/equipment can give you a competitive advantage and can help you improve your personal records.
My guess is let him freeze his butt off then have his coat waiting at the door when he realizes he was wrong. It's called letting him learn from experience.