Basically either your ISP is talking rubbish or didn't understand what you were asking (maybe they thought you were asking for ADSL without a phone line).
Possibly a couple of ISPs will want you to take the whole package (Talk-Talk is one) as they provide ADSL and voice completely unbundled from BT's equipment.
Most ISPs will give you broadband without taking line rental from them (although you do still need a phone line - in your case you pay line rental for this to BT).
Even 'LLU' providers (such as BE, O2, etc.) will allow you to take their unbundled broadband but keep your voice line rental and calls package with your existing provider.
In my case I have ADSL2+ from BE (unbundled) but I have my line rental and calls package provided by Sky.
Ask your ISP again and this time explain it more slowly (imagining you're talking to a five year old is a good tactic when ringing a call centre).
ADSL2+ with BE
DL Sync around 4.8Mbps
UL Sync 1088kbps
DG834GT with DGTeam firmware