The tow truck driver is absolutely correct. Your mechanic screwed up, I hate to say it but he did.
The CV shaft must be removed to do the job and he must have forgotten to tighten it up correctly.
Most transmission shops hire kids to remove and replace the transmission after a real mechanic builds the transmission. The kids are usually hung over or high when they do it.
I've worked in shops like this in my past and have seen it first hand.
No, it was not your mechanic's fault. You do not have to take all 4 tires to replace the transmission; the tow truck is full of BS.
I believe the tow truck driver. The axle did not break. It came off.
If you took a picture of the separation then one can tell what has happened.
I'm a lady and I don't know many things about cars. I had my 2005 saab 9-3 transmission rebuilt and my mechanic rebuilt the tranny and put it back in. The next day i'm driving the car and the axle breaks and my car just stops! My front passenger tire was almost off of the car I made a left turn and the tire was outward as if I made a right turn. The tow truck driver said it was my mechanics fault because a axle bolt was missing. The tow truck driver informed me that in order to take a transmission out or put it back in that all four tires would have to be removed and that my mechanic misplaced the axle bolt. Who is at fault?!