Council Tax reduction not possible in case of individual tenancy agreements in an HMO ?

HMO Licensing

ReG: Council Tax for HMOs

Hi,
We are owning a HMO with four tenants who have all individual tenancy agreements.
One of the tenants is only a part time student so that the she is not exempt from council tax.

Speaking to the council (Oxford) we have been informed that :
- as there is no joint tenancy agreement in place, we - not the part time student - will be invoiced for and liable for the payment of the council tax. (It would have been different if there would have been a joint tenancy agreement)
- as the property is in our name (of our ltd) and there is no joint tenancy agreement (only individual ones), the 25% reduction of the council tax bill will not apply = the whole amount is payable.

I would be grateful if you could let us know if this is correct and we would appreciate any suggestions how to resolve this situation.
There has been an agreement with the part time student that she was happy to pay the 75% council tax bill and as this would have made her flat far more expensive, we even agreed to reduce her monthly rent by £50 (as she is generally a good tenant).

Kind regards and thank you very much in advance for any help and advice