The other car was running, YOUR battery light was on? The other car's battery light was off? If that's the case, I'd blame the alternator.

But then you found the corroded connections, that can cause the entire mess. Before Kragen tested it, are you sure it was all cleaned off? Maybe you really needed the new alternator, maybe you can clean it better & test OK. (But you already bought the alternator...)

I suppose I'd trust their diagnosis, up to a point. Those corroded connections probably look just like a bad alternator, as far as their tester could tell. If you suspect they're not really cleaned up completely, clean em up & try again. Otherwise, both your battery light & their tester agree that your alternator isn't perfect. Don't forget corrosion where the wire itself is crimped into the connector...