I have used Safelite before (as recently as 5 months ago-they do very nice work) and I have never had them refuse to replace the rear view mirror. I would not pay for the job as I would consider that "incomplete". That is part of replacing the windshield.
I would contact customer service and contact your credit card company for a chargeback if necessary.
The guys were actually pretty helpful. 3 of us messed around with it after I told them I wouldn't hold them liable if the mirror broke. We all wrenched on it super hard but couldn't get it back in. We also tried to take it out of the car completely, but it seems that the V1 thing is hardwired in with no harness so we couldn't get it more than a few inches away from the windshield. I just can't believe the dealership said popping it back in was impossible and their only option was replacing the entire thing. I think the next step is popping the mirror open to see if I can disconnect all of the valentine stuff. If I can do that and get the mirror onto a workbench I'm hoping I can pop it back in without breaking the glass on the mirror. I've got a 500 mile road trip coming up on Thursday so I'm gonna try to hold it in place with some putty or something until I can find a long term fix.. I knew I would have some crazy bills with this car but I never expected the mirror to be such a mess!