Business is slow and desperate times call for desperate actions. I know of no law that allows a private business without court action to impound a car for whatever reason. Even an illegally parked car requires a ticket to be issued first before it can be towed. Simply call their bluff and call the police-at least you would get a second opinion on the legitimacy of the repair.
There use to be a time in NY where safety inspection stations could refuse to return your car if they deemed in unsafe. So basically your car was held hostage until it was fixed to THEIR satisfaction. Some states still allow this. But those states have state run inspection stations. NY and NH and MA the inspection stations are private. And there were many of these gas stations that had inspection licenses that were very unscrupulous and took full advantage of this law. The law changed, but not until they raked MILLIONS from people.