Yes, the vet tech should not have said that, what if your ("your" being anyone's dog, not just Oban) dog was super thin because he was really ill, or dying from cancer or something? That was really insensitive of her to say that to you with out any background, and way out of line.
I am surprised they allowed a sick dog in the waiting room, I sure hope she dog wasn't contagious! One more reason I wait in my car until they call me in, it should be the other way around, that sick dogs wait in the car, and the healthy ones can wait in the lobby. I once had a pregnant bitch with me and a man brought in his dog that had been vomiting and had explosive diarrhea, and she was soaking wet, because he dunked her in his pool before he left home. They let him stay in the waiting room! I immediately left to wait in my van, and this is when I started doing it.