HMO and Council Tax

HMO Licensing

I own an HMO-registered student house in Sheffield. I have owned the house since April 2013.
I have just received a council tax bill for £1300 from Sheffield City Council who say as an HMO property, I owe the council tax, this is despite it being let exclusively to students who have a council tax exemption. Sheffield say that if I send the tenancy contracts in to them they will consider my case.

My questions are:
1) Am I really liable for council tax as an HMO landlord, but not as any other kind of landlord?
2) Should I really be sending these contracts, which are ultimately private, to SCC? Do I need the students permission?
3) Surely I am not responsible for validating if tenants are students...is that not the responsibility of the Council?

I thought I read somewhere that landlords were going to have to validate if tenants were illegal immigrants, but that this proposal was stopped on the basis that it was impractical. Is my validating of students not equally impractical?

I look forward to your help on this.