Are brake shops allowed to hold your car ransom?

These shops that advertise brakes for such a cheap price, seem too good to be true and that's exactly what they are. They have low paid, less skilled employees working on your car, and will exploit you any chance they can. Mechanics should only proceed with work that was AUTHORIZED by you, and they should allow customers to get a second opinion just like a doctor. This is definitely not a legal, legitimate practice that you described - if they don't allow to take your car, I would report them to the better business bureau or even local law officals.