The communication perhaps not being from BT, nor the "engineer" that turns up.
My basic reason being yours is the first example I have seen of this, so I am suspicious. Just as in the phone calls, "I am calling from the Microsoft Support to tell you your computer is sending out viruses", and the emails from banks about your security or credit card having been compromised. If the "bank" is your own, you may think it genuine. If it isn't your own then you know.
The problems with the OR modems are well known. Perhaps someone has developed a new scam.