Q: Is it possible to damage the compressor when replacing the clutch?

I took my fiesta into the dealer for a transmission recall that was causing starting issues, they later said they were replacing the clutch on it for the recall. A couple days later, I'm told by them that there's a leak in the compressor and that they'll need me to pay for a new compressor to fix it.

Now, I had the car in with my mechanic a few days prior to taking it to the dealer, to get the starting issues looked at, and they had it for 3 days, going over it trying to figure out the problem before deciding it had to be a result of the recall, and they never saw or mentioned a problem with the compressor leaking.

Could they have damaged the compressor while replacing the clutch, and now be asking me to pay to remedy their mistake? I don't even necessarily mean intentionally, maybe they didn't realize they damaged it, or the mechanic didn't tell the inspector he did. I'm just feeling a bit blindsided by this claim.

My car has 76000 miles.
My car has an automatic transmission.