here is the thing with air mix actuators...........
GM used weak plastic for the gear inside of it. Over time the plastic gets brittle and then it splits down the middle, causing problems as you described.
So when the battery is disconnected for any reason.......when you got a new motor put in by the mechanic....the ACC system loses the air mix memory/position. When the battery is reconnected.....when your mechanic hooked it back up sometime after the motor install... the system does a full air mix sweep to regain the proper position.
The gear inside the actuator brakes sometimes because when the lose of power happens, the blend door that is connected to the air mix actuator does not properly stop...thus it fights the air mix actuator and binds causing the gear inside to break.
To prevent this from happening it is always good to physically turn off the ACC system before disconnecting the battery. This way the ACC system will properly stop where it is supposed to.
Yeah it would be great to pin this problem on the mechanic! But to actually prove it was directly his fault would be very difficult.
Unfortunately I would have to agree with him that it was just a coincidence that it stopped working.
That link I gave you tells you all you need to know to replace it yourself and save you the cost of having your mechanic do it for you. unless you don't want to mess with it than its worth what he is asking than.