No, 50% was there choice and they are not really legally responsible to pay for any of the repairs. If you press them to pay more they may retract their offer of paying 50% and not pay anything. You have to remember, they did not brake the vehicle in the first place, they only failed to repair the vehicle so they are about 50% at fault, but I would definitely have them pay 100% of the tow bill because they should have kept the vehicle and not released it until it was repaired. Now I base this information on the fact that their diagnosis is correct. Usually the cause for this issue is only a brake switch that would cost about $140 to replace. I would ask to see the old part and the new part and the invoice for the parts to be sure they have replaced something worth $1400 such as a control module.
Technician
ASE Cert, AS Degree in Automotive Diagnostics