I'm just amazed you saw a tire guy actually using a torque wrench. Closest I've seen are some mechanics using torque sockets. Usually they just use the air wrench that "someone set" years before.
If I have someone else put wheels on, I try to loosen and re-tighten them myself. I'm the one that will be having to to change a tire on the side of the road.
In answer to your questions, Yes they can easily over tighten the lug nuts.
3 consequences that can happen, among others, are: 1. Make the lug nuts so tight you simply can't get them off without large breaker bars or a powerful air wrench. 2. Weaken or even break off the lugs. 3. Warp the wheel, which is why the criss-cross pattern of tightening is important.
From what you describe, though, your wheels and lug nuts are probably fine. Sounds like a good shop you went to.