Care Assessment and Attendance Allowance

Do you have any evidence that they receive the right amount of income?

None, but I am not making any claims one way or the other so I don't need evidence. It's people who make claims who need evidence to back them up when asked if they want anyone to believe them or change anyone's mind. If evidence cannot be produced then the person making claims is much less likely to be believed or change anyones mind.

I do have evidence of how care costs works as I have it in writing.

The council would still foot the bill if you didn't claim DLA/PIP/AA. They can't expect you to contribute if you don't have the money.

This isn't true.
My MIL has very little income (about £25 per week as she's in a care home).
As the owner of a property she is still contractually obliged to pay for service charges and ground rent.
Council tax on the property also has to be paid and yes the local council do expect it.
In fact council tax on the property increased (from zero) when she went into care (they lost double carers allowance).