My brother had an account with a telephone/cable company and was disconnect due to an outstanding balance. When I moved in I set up an account with them in my name. Five months later when I moved out they transferred his outstanding balance onto my account. Is it legal for them to transfer his balance onto my account without my permission? They have explained that they are able to do so based on a "debtor on premises".

Was he living there when you moved in and was also using the cable you were paying for ?

Did you put an account in your name because he was not able to get it.

This is common to do, you can refuse to pay and let them sue you if you wish. OR better yet, get brother to give you the money to pay it

The best thing to do is LET your brother pay it. It was his debt and he should take responsibility for it.
Or if your name was also on the account then both of you pay it.

I had a similar thing happen to me, but in reverse. When we sold our house back in the 1980's the water company 3 months later sent a bill to the new homeowners saying the account was past due and that they (the new owners) were liable. They of course contacted us, and I paid the bill promptly. But if I hadn't paid, the water company would have held the new owners responsible, and their recourse would have been to sue me.