The NTPF agree the price that individual nursing homes charge Fair Deal patients. If you are approved for F/D and your assessed amount is below this figure, you pay your assessed amount and the HSE pays the balance.
As a couple your parents each owned and were assessed on 50% of their house, other assets and income. As your mum has now passed, as far as the HSE is concerned anyway, your dad now owns and will be assessed on 100% of the house (7.5%), any other assets (7.5%), and income (80%).
If they as a couple were close to the cap as you have said, it is easy to see how your dad on his own would now exceed it.
It would certainly be to your dad’s advantage to remain a F/D client. The nursing home would prefer it if he was a private client. I think I would be contacting the F/D people to discuss options and not be depending on the nursing home for information.