Apple Certified Pre-owned, but without apple warranty?

You may want to be careful buying from anywhere not authorized by Apple. A certified Apple device would come with a regular Apple Warranty but only when purchased from Apple or one of their authorized dealers. If the warranty is important to you I'd rethink this place if they aren't an authorized Apple reseller

I have never seen nor heard of any such beast as an "Apple certified pre-owned" device of any kind, not iPhone, iPad, iPod, Mac or anything else. Apple doesn't "certify" any used device.

Apple itself sells "refurbished" devices, but I have never heard of an Apple Authorized reseller having access to Apple's factory refurbished offerings. Apple's refurbishment process is very thorough and returns the product to like new condition. And, all Apple refurbished products, sold by Apple, come with a full default Apple warranty, are covered under Apple's standard 14-day unconditional return policy, and are even eligible for AppleCare+ extended warranties.

It certainly sounds to me like you are describing a non-Authorized reseller who is making up terms and advertising to push their wares. I would walk away from anything they were offering.

BTW, if you click on the small print "find a reseller" at the bottom of this page, you can find any and all Apple Authorized resellers near you. If a seller is not listed there, they are not an Authorized reseller, no matter what claims they may make to you about their company.