UPDATE:
I called the garbage supervisor today. He said having attached lids on personal cans aren't allowed due to the possibility of injuries to the sanitation employees when they are emptied (which was news to me). He also said that the pickup guy should have notified him and he would have sent a letter to that effect instead of pulling them off each time and tossing them. He said I could file and insurance claim for the lost lid.
He asked if he could interest me in the can the city sells. When I asked how much it was, he said it was $57. However, he then added that he could deduct the cost of the other cans (which are $20 each), so it will now cost me $17 and there was no mention of having to file the insurance claim. That sounded good to me, so I took him up on the offer. It is cheaper than going out to buy new cans and neither one of us have to deal with the insurance. The lid stays attached on the city can so I still get to have the hinged lid I wanted (and knowing the attached lids aren't allowed, I would not have bought the hinged kind at the store again). The new can should be delivered sometime this week.