Ridge, you're forgetting a more plausible answer which is defective installation.
I have to tell you that for a co. to send out crews & essentially pay TWICE for a re-roofing is pretty crazy. I also have to wonder what other areas they might have tried to skip or cut corners on, considering that for a large house (50 squares of walkable but not low slope (i.e. 4:12 through 8:12), you're probably looking @ $ 200.00 in 30 # product.
Compare that figure with everything else required for a full roof job...
Ridge is correct in that it's all really dependent upon how your contract is written. If they never made mention of removing old felt then they aren't required to do so. If it does state "add new felt" then they ARE required - I suspect it does state new felt somewhere otherwise the sales person or co. would have come back & said "nope" on the full tear-off they did.
Tell you what, you do something for us & we'll do something for you: Post some digital photos of your house for us (all 4 sides & far enough back so we can see any particulars like a chimney or dormers, photos out a 2nd story window onto the 1st story roof etc).
If there are spots we think might have needed special attention & they might have cut a corner on, we'll tell you to go & take a closer look or maybe pay another roofer a few bux to come & perform a quality assurance inspection. I can tell you that if you're in my town, I'd come out for free.
A few questions for you: What was it about this co. that made you select them? All of us regulars here on this forum are always trying to refine how we do business & information on how or why customers select various roofers is always a help to us.
Oh, & please let us know where you're located - @ least maybe what state.