Battery Light On

I have a 2000 Ford Focus ZX3 with a 2.0l Zetec engine.

A week ago the alternator died while I was on the road. No battery light, no warning, it just quit working. I managed to limp it into a national chain store, they tested the alternator and replaced it. A couple of hours later and $540 lighter I was on my way.

Now the battery light keeps coming on but the output voltage is holding in the 14.5 to 13.8 range. I hooked up a multimeter to my cigarette lighter so that I could monitor it while driving. I understand the alternator is controlled by the PCM. Is there a chance that the PCM is sending a false signal to illuminate the battery light? I've checked all of the obvious stuff ie:connections and battery terminations.

Semi defective alternator? Wiring damage?

Disconnect the battery = No more dash light.
Win,win.

Did they pull a Chrysler and install a battery temp sensor under the battery?

How many amps is the new one putting out?

I have the feeling while the new one "works", it is still a POS and needs to be reBUILT, not reMANUFACTURED.

And Ford sucks donkey balls on charging systems per my starter/alternator rebuilding guy.....