I always take the loose wheel in to the tyre shops. I once had a dealer replace a front tyre while they were doing a 6000m service on my bike. Rode it home (at motorway speeds, in the cold / dark / wet). The next morning I discovered that they hadn't tightened the front wheel spindle cap or even the wheel spindle pinch bolts at the ends of the forks... this was a big shiny main dealership - never went there again.Honestly I wouldn’t let a fitter anywhere near my Norton.
Also once have a tyre shop fitter put a new back tyre on the wheel with the wrong rotation, didn't spot it at the time, but very obvious when I rode the bike.