The reasons for the problem encountered by this customer are obvious; the customer was on the TalkTalk LLU!
BT had deployed FTTC to the street cabinets that covered the customer's postal address.
Thus if the customer put their 'details', namely: telephone number and postcode into consumer broadband availability checkers they would have been told that FTTC was available. What these checkers don't tend to return is the information that this conclusion was based on the postcode and not the phone line.
Using BT's wholesale checker with a phone number that is attached to a non-BT LLU will result in BT being unable to test the line and thus confirm actual service availability. Instead they will use their records and postcode information to determine if the postcode is covered by a FTTC cabinet. Thus switching LLU's, particularly from ADSL (not ADSL2 etc.) to VDSL/FTTC can be a step into the unknown.
Interestingly, my postcode suffers from the opposite problem: According to the postcode checker FTTC is not available, according to the line checker we have 80/20 FTTC (which I've had for a little over a year now). Thus I had a private laugh, a neighbour on Sky was complaining about the poor ADSL (sub 1mbps) were told by Sky that FTTC wasn't available, even though I had FTTC (from EE) installed for a couple of months at that point in time.