Medicare increases Poverty?

I actually managed to convince my professor today that my argument was a valid one. It is a warped, extremely horrible way to think about it... but in a way it is true. Without medicare the poor, who can't afford medical care, would die sooner. Medicare does not lift people out of poverty, it merely keeps their income level constant. Therefore Medicare increases the number of poor old surviving people. The poverty rate goes up. My professor told me I had a warped way of thinking about things. Possibly.