Do you know if the dealer checked the windings with a meter by unplugging the big multiwire white connecter? If he just asked the symptoms and came up with that, you may be taken for a $$$ ride.
I ask because while that is the worst $$ way the gen can fail suddenly, there's at least one other way (voltage reg, easy fix, one hidden screw, about $250 part). And believe me, I know your frustration! They completely rebuilt the electrical part of mine under warranty due to a similar failure at _8_ hours. IIRC, Onan was billed about $1600 for that. That's when they left the bolt loose and left a mount out.
And yes, you may have a low oil float switch as retraite said. They discontinued that sometime in the past, but I don't have a clue as to when. And it _will_ give the same symptom. If you have an owner's manual, read the proper procedure for checking oil. Mine ('06) requires you to remove & wipe the dipstick, then set it on the hole, not screwed in, to check the level. Screwing it in before reading will give a false reading resulting in low oil.
And trust me, I'm not particularly wrench savvy, just persistent... ;)
Jim, "No, the other one."