If my 17 year old son wrecked his friend's father's vehicle and the friend gave him permission to drive it but is now saying that he didn't, what are we liable for?
At a minimum, your son (and therefore you, since he is minor) would be liable for the cost to repair or, if it can't be economically repaired, the current fair market or blue book value of the car (i.e if it needs to be "totalled"), IF your son was at fault in wrecking it--that is, if he was driving in any way carelessly (too fast for conditions; faster than speed limit; ignored stop signs or lights; texting while driving or DUI; etc.). Your son and you could also be liable for any injuries; for any other costs coming out of the accident (e.g towing; car rental); and for damage to anyone else' property (such as if he hit another vehice or someone' fence).
If you son was not at fault--e.g. another car, which was at fault, hit them; or the car crashed because its brakes gave out--he should not be liable UNLESS THE "friend" can convince the authorities that your son actually stole the car (which is what taking a car without permission is). If the "friend" can do this, then your son and you would be liable for all costs, regardless of fault (someone who takes a car without permission is responsible for everything that happens to it); your son could also potentially face criminal liability. You may wish to retain an attorney to help you and your son.