2002 Chevy Cavalier Tapping noise: AC unit or Timing Chain

Noises problem
2002 Chevy Cavalier 4 cyl Automatic 130000 miles

I have had a tapping sound coming from my car for about 2 years. When I purchased the car it was making (what I thought) was the same noise and I took it back to the dealer and they said that they replaced the timing chain tensioner. It quit tapping for about 3 weeks in which time I moved away and could not get it back to the dealer. It taps about 90% of the time and only occasional does not when you turn it on but the silences only lasts about 5 minutes. I took it to the garage last week to get the AC unit replaced and also to get the tapping noise fixed. I researched, watched videos and spoke with tons of people to see what the noise was for months and most people said it was the timing chain and that it was slacking and making the noise. Some also thought it was the lifters but using Lucas and even the best oil did not even make the smallest difference in the sound.

The garage just called me and said that he looked at everything and he says the source of the tapping turned out to be the bad AC unit and it is being replaced. He is putting it in tomorrow and said that it would fix the tapping.

My problem/question is: how is this possible? Not one person(even experienced mechanics) even mentioned about the AC unit. I have watched videos of cars of the same year with the same noise coming from the same area and it was the timing chain. The garage said that the fan constantly runs and that it was the source of the sound. My question is how does the fan always run but it only taps about 90% of the time? Also, when the AC unit worked it STILL tapped.

I just know when I go and pick the car up tomorrow its still going to make the noise. The main reason for taking the car there was to get the noise fixed but I said while you have it apart just fix the ac. I just have a feeling that he did not want to do the time consuming, tedious job. If I would have never mentioned fixing the AC I do not think he would have said that was the problem. I think he is just dragging me along because he thinks I have no idea whats going on. I may not be a mechanic but I am intelligent enough to do research and I understand how a car works. Also when he first took the car in he told me he had to fix the ac unit first to see if that was the problem. That sounds a little weird that he can not inspect/listen to a car and diagnose it. It just seems like he does not want to fix it which is fine but dont string me along and complain about a pulled muscle all week.

If I pick it up tomorrow and the sound is gone I have no problem admitting that I was wrong but things just are not adding up. I would be super happy seeing that he fixed my supposed $900 job for only $170 but I am paying for a rental car for a week and if it is still making the sound I do not know what to do.