If this is a second-hand phone, and still logged into the Apple Account of a previous owner, that owner could mark the phone as Lost, turning it into a useless "brick" as far as you are concerned.
This is something that might happen if the owner did not part with the phone willingly (i.e. the phone was lost – or stolen).
Whether or not the phone is associated with someone else's Apple Account, a carrier could blacklist it, rendering it unable to receive cellular service from any carrier who honors the blacklist. This might happen if
- The phone was reported lost or stolen, or
- A previous owner bought the phone with carrier financing or subsidies, but failed to meet contract requirements
As far as the seller saying that they will contact Apple's fraud department to try to have your phone disabled, I am not sure what they are talking about. Did you give them any reason to want to do such a thing? For instance, did you pay for the phone with a check that bounced?