Bought a used iPhone with AppleCare+

Here are details:

Transfer your AppleCare plan - Apple Support

But I must say the "We're sorry ..." message you cite above looks very suspicious. Be certain you can get your money back if there is something not quite right about your purchase.

The response you got implies that the owner's phone was replaced as part of service, and the phone you have was then legally obligated to be returned to Apple. It seems the owner did not do that, in which case, it is technically a stolen device.

This is not an uncommon scam on unregulated web sites. People get a phone replaced under warranty, and are then obligated to return the damaged device. But instead they try to make a buck by selling it. In the USA those devices usually end up carrier blacklisted as well.

AppleCare may be the least of your problems. Check to be certain the iPhone is not Activation Locked. If it is Activation Locked, and you cannot contact the original owner (which would be the case, for example, if the iPhone were stolen before you purchased it), you will never be able to use the iPhone.

See especially "How do I check for Activation Lock before I buy a used device?" here:

Find My iPhone Activation Lock - Apple Support

No, Apple won't get involved with private party sales or exchanges at all. If what I described is what happened, then it's a matter for the police, as that device was contractually required to be returned to Apple in exchange for the warranty replacement device. As I said, it would be considered stolen at that point.

Unless Craig's list offers some sort of recourse, which I don't know as I don't use them (for reasons just like this).