The ISP pays BT for use of their lines and bandwidth.
The ISP then use servers, admin staff, staff to provide a helpline, staff to keep the servers updated and functioning well. They provide dedicated servers with backup and altogether keep things running smoothly.
In short, a good ISP does NOT rely on BT to be the be-all and end-all for everything, they actually make an effort and liase with BT should BT present a problem.
Cheaper ISP's rely on BT too much and are only concerned with incoming revenue.
Decent ISP's niggle at BT and make an effort. And that's why you pay more for a good service.
Simplistic, but true.