I was thinking that's how OP meant it, but that still doesn't match the sites claim. And yes, I know the site is stupid and wrong, but its not self-owning. The site is saying that the 355k is paid by individual families, and that cost is clearly greater than buying private insurance would cost anyways, and just generally untenable for most people regardless of the other benefits. So the site is saying "you'll be forced to pay 35k each year". It denies the idea that taxes on billionaires would cover the cost. So it is exactly claiming that we take the burden on individually.

The website is internally consistent, it's just wrong with respect to reality. But it doesn't contradict itself.