No concern. Water running is to flush away the ground food, not to lubricate the mechanism.

Part of the purpose is also to cool the unit, but if it was still running it's probably fine. Disposers have fuses that go off when they get distressed by jams, overheating, etc. There's a little red button underneath to turn them back on again after you tend to the issues. If you have the red reset button, but didn't need to use it, there's probably no harm at all. It's grinding away forever on a bone that's too big or hard for it that's going to be the problem. Insinkerator advertises that you can put a pineapple top through it. Your plumber will say don't you dare! But that's what the resultant mess will do to your drain pipe, not whether the machine can handle it. :)

I think the water also protects the seal to the motor. I would insist that the contractor replace it so you don't have a problem later on.