hard to say without inspecting it yourself. If the axle cut loose, it might have damaged some other part of the car, but a visual inspection should be able to tell. I don't think anything internal could be damaged, but it might have banged up the suspension or flanges where the axle bolts to. The shop should let you under the car and you can all check it out together. I would think they'd be happy to make you happy at this point.
Yes rebuilt axle is an acceptable solution. You might want to think about doing the other side as well, if the car has high miles.