For the second time in a week, I got somewhere in my 1993 190E 2.3 and it wouldn't start after driving it somewhere

I took the battery to have it charged and tested (it tested good). So when I got it home, I let it run and pulled the positive cable off, and it continued to run (it tests at 15V on an analog Voltmeter that I have). This is a fairly new battery (back in the winter) but the car sat up for the last month and a half because the radiator was bad (drove my diesel instead as diesel was cheaper for a long time than premium gas anyways). So while I had the positive cable disconnnected letting the engine run off of the alternator, I turned the headlights on and it killed the engine. Its a 70 amp alternator, so I'm guessing it should run the engine and headlights (nothing else on, no a/c, no radio, etc) correct? Does it sound like the voltage regulator on the alternator is gone south?