It's no joke; it's exactly what happened to me: leaking coolant plus a small PS fluid leak lubricating the belt and causing it to slip, which negatively impacted alternator, water pump, power steering and A/C performance.
Zorro's subsequent post confirms the validity, except his belt is slipping because it is too loose, rather than too lubricated as mine was.
Zorro: your alternator guy's assessment is probably correct. If the atlernator (like any generator) spins too slowly it puts out less current. If the water pump is spinning too slowly it cools less efficiently.
If his belt tensioner is not broken, you have a very easy problem to resolve: simply tighten the belt, or replace an old "loose" one (if such a thing is possible) with a new one.
What constitutes "loose" is the question. With some moderate effort, I can lift my belt up and off of the pulleys, yet the tension is proper. To cause slippage, it would have to be quite slack.
Zorro, is your steering also kind of heavy? (You should be able to turn the wheel lock to lock with one finger when the car is idling.) How about your air conditioning -- is it performing optimally? These are belt-driven and should be equally impacted.
If the belt is chewed, replace it immediately; it will break at high RPM. If you don't believe me, shift into 2nd and drive at 40 or so MPH/5000RPM for about a minute. The belt will cheerfully disintegrate. (Trust me; I know.
) And your engine will instantly overheat, and your block may possibly crack. Not a happy day. (Fortunately, that is one which I have NOT experienced...)
Replacing the belt is very easy and very cheap: about $30 for the belt and perhaps 30 minutes time ($37.50?) if your mechanic does it, or just the cost of the belt if you do it.