Company A are responsible for collecting the TV Licence Fee.
Company B are responsible for issuing the TV Licence (physical evidence that payment has been made and received).
A tell B that congming88 has paid in full, and B issue the licence.
If B has failed to collect the money from congming88, then although he has a TV licence, it has NOT been paid for and is worthless.
Unless congming88 can 'prove' that payment was made by him to A for the TV licence he will be seen as a 'defaulter'.
Although, he is under the impression that it has been paid for, he is also NOT confident enough to tell Capita to stuff it.
I would satisfy my own mind that I had paid, and then let Capita chase their own tails in trying to prove otherwise.