I, um, ah, think he may have charged you to check the muffler bearings as well. Although what you describe is theoretically possible, I have never heard of this being done.

Here is a video that show what you clutch does:

https://www.youtube.com/watch?v=N_GkuTgJr3w

I would be more inclined to believe cleaned the radiator and coil. If you have a 1993 or retrofitted AC he might have gotten the secondary electric fan working again.

Now if you had told me the AC compressor clutch needed grease, I actually would had to look that one's operations up before getting so gosh darned skeptical, but adding grease to a viscous fan clutch really does sound like rotating the air in your tires.

All that said, I found a couple of you tube videos on how to change the fluid so I may be the one being to cynical.