Medicare covers only a minority of the population but (and?) relies heavily on the general US private healthcare system. At minimum, Medicare cost is affected by high drug prices (perpetuated by lobbying-influenced government avoidance of price controls), relatively high coverage denials (which Congress and the executive branch refuse to regulate), and lack of vision or dental coverage unless people use "Medicare" Advantage (which currently gives private insurers too much leeway to raise costs for the government without a corresponding healthcare benefit [1]).
Anyway, I think parent comment to yours is using single-payer in the sense that implies universal healthcare [2].
[1] https://www.kff.org/medicare/how-medicare-pays-medicare-adva...
Drug prices are less than 10% of all US health care spending. Drive all drug prices to zero dollars and we get a grocery store circular discount on total health costs.