Dont ever expect tax credit people to get things right.
I worked there once, it was part time job in the evnings hot desking with the fulltime revenue staff.
My section of about 25 was mostly made up of schoolkids who came straight from school, and
a large number of women who seemed to be doing the job just as a way of getting out of the house and socialising. If you gave the same claim to everyone in the section you would have had 25 different results. I saw it as a possible career, it was my only income and very important to me,
but no one else seemed to take it seriously and realise that they were playing with people's lives.
I used to get letters from people like yourself saying that they were sure they were being overpaid and could they please stop receiving money, but we weren't allowed to stop their claims!!

A claim could only be stopped if they gave a legitimate reason, ie they no longer qualified.
As for traceability it is very easy for someone to change the history of comunication on your computer file, there is no big folder with all your letters and stuff in it. Claims and renewals are dealt with at different offices round the country, as are changes in circumstances,
it is quite possible that details you provided were entered onto the system without anybody even looking at your missus circumstances, thats why the anomlay of you receiving JSA would not have been noticed, that and the fact that a group of monkeys would have as much chance of coming up with the right figure than the people they employ.