The advice you have been given is correct.
What you read about disqualifications being spent at the end of the ban only relates to disqualifications for non motoring offences, so for offences like TWOC.
They realised that if they made disqualifications for motoring offences spent when the ban ended, they would not have to be declared for drink driving and other motoring offences for insurance purposes, so they exempted those offences from becoming spent when the ban ended.
That means that criminals are forgiven quicker than motorists are!!!!