TCGS:Am I surly not right in saying I could phone them back now, demand proof that I owe them money and if they can't provide me with the proof immediately, then the debt is non existent?
It's best to do it by letter, asking for "full details" rather than "proof", in my view. It's not unknown for large organisations to be "unable to find a record of that telephone conversation" when it suits them.
They do not have to provide details immediately but they should not pursue the matter further until/unless they can provide details.