This once happened to somebody I know! Their Apple ID somehow got banned from specifically, and only, iMessage and FaceTime; all other services like iCloud and the app store were working as usual.
No idea why it happened, but Apple support was able to reset it on a phone call.
My theory is that they'd kept a non-active SIM in their phone for a long time, and the phone had tried to repeatedly verify/link that phone number to their Apple ID (via challenge SMS, I believe), thereby exceeding some rate limit.
Gotta love that such rate limits exist and do occasionally hit legitimate users, but at the same time, there are paid lookup-as-a-service APIs out there as mentioned in TFA...