"I was told by a gentleman the first time this happened(after hand cranking for a couple minutes) by pushing he car the generator produces enough power to start the car. Is this accurate? "
Yes, that's accurate and a nice thing about generators. When I was 12 and had my dad's old 1950 Studebaker for my field car I did a lot of push starting. Dad finally picked up a good 6 volt battery at the junk yard for $5.
Mitch gave good advice about checking for a bad cutout. If you don't find a bad cuout or some other draw, then I'd look into a bad battery. When a battery is dead it should be put on a slow charge (6 amp charger or less) for at least 12 hours. Generators and alternators are meant to supply the current used during driving and aren't made to be battery chargers for dead batteries. At the junk yard where I worked the loader operator would often run the batteries down to dead or almost dead, after he'd run the loader out of diesel. Then instead of properly recharging the batteries he'd jump start it and let the 24 volt alternator recharge the batteries. He burned out several alternator regulators doing this.
BTW, since you have a voltage regulator you will be OK if this happened at night and you had to use the lights right after starting the car with a dead battery. For those not using a voltage regulator, it's not a good idea to use the lights until the battery regains a fair amount of charge. A dead battery has a lot of resistence and very little ability to control the voltage output from the unregulated generator, so you may burn out any lights that are turned on. When I first bought my early 29 Tudor the battery was so worn out that it couldn't control the unregulated output of the powerhouse generator. Even on the lowest setting of the adjustable brush it was putting out 10 volts all the time. That's why I desided to start making elecronic voltage regulators to take the place of the adjustable brush.