Council tenants contribute to social care too

I don't agree with the Tory policy of making home owners pay for social care by having to pay all but £100 thousand pounds of the value of their homes to the local authority after they die. However, I have heard several people, both on the radio and on the doorstep while canvassing (for Labour), complain about the policy in something like the following words:
"Why should I, when I've worked hard all my life to be able to own my own home and have something to pass on to my children, have to sell my house and give most of the money to the government in order to pay for my care, while someone who lives in a council house will get the same care completely free of charge?"
As someone who lives in a council house, I find this view very annoying, because it is based on a complete misunderstanding of the situation. Let me demonstrate with some simple calculations. I realise rents and house prices have been lower in the past than they are today, and they may be higher in the future, but for the sake of simplicity I'll do the calculations in today's money.
My rent is currently £620 per month. I first moved in to a council house when I was 22, but I spent some time unemployed and some in private rented accommodation, so I'll write off three years and start my calculations from the age of 25. So someone, such as myself, who moves into council accommodation at a cost of £620 per month and pays full rent from the age of 25 until the age of 67 (the retirement age for people, such as myself, who are reliant on a state pension and who will not retire before 2028) will, by the time they retire, have paid a total of £312,480 in rent - all of which goes back to the local authority (the very body which is responsible for social care). This is the equivalent of what someone who owns a home worth £412,480 would have to pay. Like the home owner, the council house tenant will have no home of their own left to pass on to their children, in spite of all that money they have paid throughout their lives. But unlike the home owner, they won't have £100 thousand pounds of assets left over. Furthermore, this will be the case whether or not they require social care.
I don't agree with the Tory policy, because I believe health and social care should be integrated and free at the point of delivery for everyone, but I hope I have demonstrated that just because someone lives in a council house does not mean that they are somehow free-riding at the expense of homeowners when it comes to paying towards the care that we may all, some day, come to rely on.