council mistake in decision who to pay HB to

the private T stopped paying rent, but L found out T was getting HB.
I contacted HB asked for direct payment as 2 months unpaid proven by bank statements.

The T duped the council by showing a late rent payment, that made it appear as a recent payment.

So the council made an error and continued payment to T.
This scenarion happened again at the next month
Council now admit the errors after i insisted on meeting them to clear up their confusion.
They will pay direct from the date of suspension but not pay for their mistakes.

Quote

"With regard to past payments. Where a decision is made to pay housing benefit to the tenant, there is no provision within benefit regulations to make a second payment for the same period to the landlord. If it is subsequently decided that the payment should have been made to the landlord, any payment already made to the tenant for the same period is offset against any further payment that may be due for that period. The net result being that no further housing benefit can be paid for that past period (regulation 98(1) of the Housing Benefit Regulations 2006)."

what do you think, should they backdate it ?