First off, stuff like this sucks for ever and I'm really sorry to hear this happened to you. As you said there's insurance to pay for accidents. Sh*t happens and the joke shouldn't be on you as a customer.
When I read through your description, I found one detail fishy right away:
The wheel was already ON the machine with the new tire put on, when the tech walked up to you to make you aware of the damage. If he was an honest guy/company they would check this PRIOR they put their hands on your car!
Remember when I rented a car on Spain? There's a sheet to fill out and note ALL existing dents and scratches on the car. If that's not done, I will not get on the car because you never know if they want to sew you.
For reference here's a damage caused by a curb, which
Clonehead already mentioned above. My dad had a discussion with a client and didn't pay full attention while parking. That rim is $500 so he bit his tongue quite a bit after this.
To me your damage looks different, because it's a smooth bent for a lack of a better word. I could ask a mechanic here in Germany what he thinks of your case.
I hope it'll be figured out, but it's annoying nevertheless...
Best wishes and be safe everyone!