I could be wrong, but I did call AT&T last weekend when the iPhone 4 refurbished became available because my cousin was interested in one, but she doesn't know what questions to ask, so I called for her.
The woman on the phone "Looked into it" and told me that I only have 90 days warranty, no option for Apple Care, and they are sold as is (whatever condition they have available).
I'm only going by what I was told, and what I've read online, but don't hold me to it.
I did some more Googling. It looks like the 90 days is guaranteed, but is an established minimum on coverage. So, if you buy a refurbished unit and enter its serial number into this page (
https://selfsolve.apple.com/agreementWarrantyDynamic.do), and it turns out there's only a month of coverage left, Apple and AT&T will bump it up to 90 days.
If, instead, you enter your hardware serial number into that website and it says 11 months, you inherit that.
I've also heard stories online of people contacting Apple or going into the store with their refurb receipt and just getting bumped up to the nominal twelve months. Likewise, I've heard no problems about purchasing Applecare, since Apple doesn't even know or care whether or not the device has been resold (hence the earlier coverage from the original owner's Applecare running onwards from the first activation.)
I think AT&T's policy here more regards their other phones, for whom they're the ones who normally provide warranty and insurance coverage. Apple having a big role here makes them a strange middleman, as we've often seen with other issues.
Anyway, it is a strange headache and a possible set of hassles. But I save $50 (which normally isn't a big amount, but right now am pinching pennies) and I lose out on the pretty Apple box. Oh well.
I figure if there are real issues with the phone, the Genius bar will replace it anyway (as they seem fond of doing for people with even "minor" reception or proximity-sensor issues).