03 chevy cavalier jumped time

So I posted here about my engine fan not
kicking on. While I was driving it a few days
ago, I was making a turn and the car
suddenly cut off on me and would not turn
back on. Checked everything I knew to
check including oil and while a little past
time to change there was still oil at the
proper level. Led me to believe it was the
fuel pump since there was no audible click
when I went to turn the car over.

I have a service plan with my car loan
company that sold me the vehicle who
takes care of such essential mechanical
breakdowns. I had them tow it to a shop
only to find out this morning that the shop is
saying there isn't a drop of oil in my motor
and that caused it to jump time and that the
motor needed to be replaced.

I have had a car jump time before and I
know what a vehicle sounds like when it is
low on oil. I know how to check for oil leaks
beneath the car and haven't noticed any
since I got the car and I've been checking
the oil about every other day since the
engine fan stopped coming on. There was
no burning (the characteristic white smoke)
and it has stayed at the same level.

Is this possible? Or is the service shop
trying to scam my car company by making
them pay for something they are legally
obligated to cover?