Did she perhaps mean the minimum that is the going rate for that type of house in the area?
If she ment peppercorn rent of only a few pounds a year then that is to be decided between themselves.
If your grandad passes away then who will own the house? If it will be nan, once he has gone, then she (through your aunt) may be forced to either sell the property or charge the going rent to pay for her own care home fees.
If nan has enough assests to pay for her care then whatever rent is charged is charged.
When grandad goes perhaps your cousin could offer to buy the house at 'family rates'.