I used to do both, plug and patch, not just on cars but semi tires as well. Patching is the best but costs the most because the tire comes off the rim, then needs to be re-balanced, where if you plug, you can do it sometimes right on the car. On my own cars and anyone I fix a flat for on the road, I cary a jack, $20 compressor, and a plug kit with me at all times, and if done correctly can last the life of the tire. I have yet in ANY of the tires I have done come back because they still leak, but then Im not a pot head tire jockey and take pride in any work I do, and even when done I re-check my work to make sure when my stuff leaves its not leaking at all.
You dont need to buy a new tire and waste the money, but since its already been reamed, Im guessing if they did their job right, you will need to find a shop that patches with a PLUG PATCH, its a patch with a plug end in the middle of the patch. Prolly cost you around 25-40 beans depending on the shop, and will last the life of the tire.