Absolutely. The state cannot pay for everyone so it's fair that those who can pay for their own care should do so. I won't get involved in discussions about what people should or shouldn't do with their money - that's a slippery slope and everyone has their own opinions.It's the system that's wrong not the person in the room next door.
But paying twice over to cover the shortfall from council funding (i.e. paying tax AND paying an extra £200 per week for a room) is just wrong. Mum's money should all have been for her own care. It's like mum was paying a top up for her neighbour!