I have used a resistance battery tester and a test with a Innova OBDII tester. The Innova has a test for both the battery and alternator.
The obd is just polling the computer, I wouldn't rely on that at all
Checking voltage without any draw doesn't really tell you the condition unless it's totally fubar'd, key on position isn't enough load, and running, the alternator is masking and battery troubles
I would crank that guy with a multimeter on it and see what sort of voltage drop you get at the terminals, and again at the solenoid, that should eliminate bad battery, bad grounds/power lead
When I say the resistance tester, I mean the one with a big coil that smokes like a banshee because you have inadvertently gotten oil all over it...that's probably the best although not perfect tester