If they are old enough to drive - they are old enough to have the responsibility of maintaining the vehicles (including tires, oil changes, tag and safety inspections), getting insurance and buying their own gas. Privileges, in general, have responsibilities attached.
ESPECIALLY if there is attitude involved - lol.
I do not see it as throwing xah under the bus. I see it as your boundary and setting limits on what the children can "expect" from you. I think it was a legitimate statement.
Seems the kids may have taken a play from xah play book and xah is playing the disney dad part (i.e., I'll be the good guy and get you a vehicle - regardless of what else is involved and then make mom to be the bad person when she won't cooperate).