1998 Oldsmobile Cutlass A/C switch faulty

I was told that it is a common problem in the olds that the switch goes bad. A/C kept cutting off. It was replaced just b/4 I took it on the highway on Sat., and I broke down due to engine over heating. The belt had come off and I was told by the police officer that it runs the whole engine. He said that to repair the A/C the belt had to be removed and, apparently, it had not been reinstalled correctly. Is this true? I had it towed a hundred miles back to the repair shop.