No one said it was BT's kit causing the problem. It will be the copper line that is picking up the interference, not the OP's router.
Openreach have zero powers to make someone turn off or replace any equipment which may be causing the problem.
If Openreach cannot resolve and as a result BT cannot supply the service, then the OP will be offered out of their contract. Simple as that.
Not sure your analogy in point 3 makes any sense.
Edited by lee111s (Tue 25-Jul-17 09:53:23)