"You will not be counted (to pay council tax) if you are the spouse, civil partner or dependant of a student, are not a British Citizen, and are prevented by the terms of your permission to be in the UK either from taking paid employment OR from claiming benefits."
The problem with the argument being put forward is that it is equating "Public Funds" with "benefits". But in fact there are many benefits that are not within the definition of "Public Funds". Accordingly it follows that the person is not prevented from claiming benefits, only some benefits.
For example, in respect of the sort of couple we are talking about here, if they have any children, no problem claiming Child Benefit, and assuming their family income is low enough, the couple making a joint claim for Tax Credits.
Therefore it is my opinion that Councils that have granted total exemption from Council Tax, for the couple, I think they have wrongly granted that total exemption, and only a 25% discount should have been given.