Even basic electricity is often misunderstood by parts-monkeys. I would always take their advice with a grain of salt.
EricF has pretty much covered all bases, but I'll re-word some of it.
A 100-amp alternator is rated at its optimum RPM. Can't say exactly what that is, but it will be well above idle. So a 100-amp alternator will not be able to put out 100 amps at idle.
The amount that your alternator puts out at ANY RPM is a function of how much current is being drawn by assorted vehicle circuits, but will be no more than the maximum output of the alternator (whatever that happens to be). If current draw exceeds the capacity of the alternator at any RPM, the battery will take over temporarily, albeit at a slightly lower voltage- which will show up in the form of dimming lights and such.
When an alternator is tested ON the vehicle, you usually turn on the headlights, blower motor, a/c, rear defroster, etc. to load the alternator, then check the amperage output and the voltage. If the alternator is putting out quite a few amps (this will be a guestimate, but 39 is plenty), AND voltage is roughly between 13.5 and 14.7 or thereabouts (opinions will vary on exact voltage requirements), then you have a working alternator. Now, in MY opinion (and some will disagree with me here), the amperage check isn't really necessary (though it's good for verification). If you turn on all vehicle accessories and still have around 14 volts at the BATTERY, then you can pretty much assume that the alternator is doing its job.
So what's the symptom that we're trying to shoot down here? Just slow cranking/not starting in the morning? If that's the case, then you've pretty much eliminated the alternator as a problem. Parasitic (key-off) current draw is a possible cause... but in my experience, 90% of the time, starting problems can be traced to a bad battery and/or bad connections. That's where I'd start.