2004 Civic - Internal comp. Affecting A/C?

A/C blows out hot air, originally told it needed an a/c recharge, which was done. The next day it was still blowing warm air. Took it back today, they are now saying the internal computer isn't sending the signal to the a/c, and they don't know why, but whatever it is is going to cost $975. What's the deal, is that legit? Sounds shady to me.