question about digitizer cracked and if touch response still works

Now I'm not saying I'm right, but here's my input.

If the glass (I'm assuming it was a cover for the digitizer) was cracked, then the glass part was cracked. The digitizer is usually part of the assembly, so you'd have to replace both parts. Again, not saying I'm right, as I've never owned one of these, but I'm trying to speak from experience.

The digitizer might've had some cosmetic damage, as they had said, but if the phone's touch display worked when they tested it, then the contacts the digitizer uses weren't broken. It doesn't happen often, as the digitizer is usually one of the most delicate parts of a phone or tablet (or touchscreen pc for that matter). I've seen a couple phones survive cracked screens but the touch sensor still worked.

A cracked screen but a functional touch sensor is one of those "one-in-a-hundred" instances. Its always an instance of "test it before you judge it," in my experience. I've got a tablet right now with no visible damage, yet the digitizer has plenty of dead-zones that fails to type correctly or accept touch input variably. Just because its broke, doesn't mean that it is.

I'd say that's a safe bet as-is, but if you can, see if the entire digitizer can be replaced too for a little bit extra $$$, just my personal recommendation. A cracked digitizer is like a countdown until the crack gets bigger and actually breaks the touchpad for real.