Roger, the only thing to do is relax.
So 'they' want all sorts of impossible sums, 'they' have no option but to make their demands. The system is one designed to accommodate the wishes of both sides in Parliament.
The people one speaks to, that may say "It's not my problem", are reporting a fact, coupled with an attitude of self-defence - 'they' each and all know how crazy it is, 'they' get exactly the same phone call your brother made all through their working day.
The one glimmer of hope in all of this is that your brother is by no means alone. See link below...
http://www.which.co.uk/money/tax/guides/tax-credits/tax-credit-overpayments/