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Don't buy it. That means that the phone was stolen, or was reported as defective and replaced, but not subsequently returned to Apple as required.

Apple will not service it under any circumstances.

In most cases, what you said is true...however, this is not always the case. Take myself for example...

1: I posted my phone online to sell

2: Someone saw my serial number and called AppleCare to get a replacement phone

3: An inferior AppleCare representative bypassed a component validation (check serial number to the device on hand) and approved the replacement under my AppleCare plan.

4: After noticing this (about 4 days after it happened) and a trip to Apple and a call to AppleCare, all was resolved. My phone is back to being covered under AppleCare+

5: I learned my lesson.

So, as you can see, there is a chance that it can be something else. Although, if the person selling the phone notices, it shouldn't take long to resolve it. Chances are that it is what you said.

Hope this helps