If you can show that your last requisite oil change was done by another mechanic instead of you, then it may be sufficient to prove that these new guys are the proximate-cause of the problem regardless of their claims otherwise. But I digress…
Yes, re-tapping it in my opinion would be the most proper versus the cost. However as a lifelong friend of JB-Weld I would do it even cheaper myself. I would drain the pan thoroughly, then with a gas-soaked rag thoroughly remove the remaining oil around and behind the hole. Then dab JB or other cold-weld material on a new brass fitting I could get at any plumbing supply. The fitting could be reverse-thread and just slightly larger than the hole so it would self-tap and hold strong. Let set for at least 24 hours. My total cost on that is estimated around $12. I would guess any honest mechanic would still want around $80 to do it the previous way.
Good luck.