FWIW, I don't trust Ford (in my area) in testing anything. I had the same thing happen and got the same results as you. I had always wanted a new high amp alternator so I bought one. While at the alternator shop, I had them test both the new model to make sure it was working and the old one to keep as a backup...the one Ford said was good showed bad
Later when the batteries gave out and were causing problems, 2 dealerships in the area swore my starting batteries were good. Even though I told them to pull each battery and check each by itself, they lied to me and said all was OK. The seperator I had at the time was automatically assisting the starting of the engine. When the smell of sulfur appeared, I knew one or both starting batteries had gone south. Took it to a friends shop where we dropped both batteries and found one good and one completely shorted out. Installed 2 new batteries and everything finally came back to normal.
Glad you singled out the problem.
Dave B