Palmetto 57 VW Wouldn't let me get independent inspection; then starter in car failed next morning...$770 repair! miami Florida

We traveled 1 1/2 hours to Palmetto 57 VW in Miami to purchase a used BMW we saw on line with 49,700 miles. The factory warranty had already expired.  We requested that we be allowed to have it inspected by an independent/impartial mechanic.  They said it has already been inspected by them and wouldn't allow us to do so.  Thinking that they must be a reputable dealer since they are a VW franchise dealer and that their inspections are thorough, we purchased the car anyway.  

The morning after we got home, it wouldn't start.  We had it towed to another facility close to home and found out it's a bad starter...a $770 repair!  We called them and they will not pay the repair bill.  They won't even stand behind their cars for 24 hours!  Makes you wonder...why wouldn't  they let us get it inspected elsewhere?  This smells.  It appears as though they just wanted to get it off their lot and make it somebody else's problem.  If they won't back up their product for at least 24 hours, what will they do to you?  Would  you want to do business with a company like this?  They apparently don't care about their reputation.