2 pointsAlmost positive they lied to you and it was the power connection to the turn signal filament side, most likely just the contact in the bulb socket needed a little tweak or cleaning. If the ground was bad you'd have no light, or both filaments would light very dimly if the circuit allows it to pull ground through the rear turn signal.
1 pointAhh. You said it was "on for normal running light" and I assumed that meant it was normal light output on the running light. Dimly lit would indicate a loss of ground, and I'll bet the right rear was also dimly lit but there's no reason you'da thought to look at it. $80 seems steep to me. When I see stuff like this I wish I could live near everyone that has a small easily cured problem, that's the kinda shit I fix in my driveway for a beer.....and since it's my driveway I usually end up supplying the damn beer. Maybe I should rethink my business approach.