Glad you took that ribbing as intended.
As far as damaging the rivnut during the welding process, you just want to make sure they aren't using a stick welder. That would be way too hot and likely melt the rivnut. It needs to be welded with a MIG welder so that they can adjust the setting low enough to match the size of the metal they're welding. Any competant welder will know this. We're just talking about three small tack welds around the head. If he cools it with a wet rag after each spot/tack weld, it should be fine. You do want to sand or grind the frame to bare metal around the head of the rivnut so that he isn't welding through paint and grease though. It can be done but would require him to turn the welder up higher in order to arc through the layers of paint and grease and it would not produce as good a weld.
I read on the web page for the rivnut tool that the rivnuts are made of very strong materials. This and the fact that the head is pretty large in diameter makes me think that it should accept 3 or 4 decent tack welds done properly just fine with out affecting the threads.
You seem to have confidance in the person at the muffler shop. But, just so that you aren't dissappointed, I'd spell out exactly what you want done and how you want it done when you ask for a price for doing the job. IE, use a MIG welder and 3 or 4 good tack welds, cooled with a wet rag after each one so as not to damage the rivnut.
I'd grind the frame to bare metal around the head myself to save him the trouble and so that you know it's done. That way, all he has to do is push the nut up into the hole and make 3 or 4 tacks, cooling with a wet rag in between each one. Once it's up on the lift, it shouldn't take more than 5 minutes tops.