Hi,
There are two possibles.
1) Your ID is not logged into iMessages properly. There is no way in the app to tell until you either start a new Messages and contacts go red (and "Not registered with iMessages")or your try to send something and it gets the "Not Delivered" alert.
It is fair to say the info you are given suggests the issue is at the other end but that is often not the case.
2) they have in fact de-registered their iPhone.
This can happen if they move the SIM card to an new iPhone. This keeps the same number but does not access iMessages properly as the Serial number appears to be involved in a secure connection.
Or the Settings > Messages > Send and Receive can have the number Unticked (it shouldn't as the user can't change it but I have seen it twice).
This would be on their end.
Your only option may be to contact Apple Support.
This too can be a long an protracted operation.
You have to state it is an Apple ID issue. (There afre free to fix)
However you will be speaking to Level one responders who are script led and looking to solve peoples Apple Care problems with Software and Hardware.
Most likely you will have to specifically ask to speak to a Level 2 person.
Back in Mountain Lion these people would be able to check the server and reset your Apple ID login as it only effects the Mac.
Now there are several instances where this can happen and often they involve the Engineers as they try to find the cause.
Most people who have reported back on this have posted they have had to wait overnight/24 hours and have been due a follow up telephone call that they don't get.
8:50 pm Friday; November 27, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad