It isn't true any more, however. You can outlay money to increase your life span down the line - though it isn't an individual thing, it is increasing life span for everyone. It is a collaborative effort.
How: money can be used as a lever at all levels of research and development in the science of aging to increase everyone's life expectancy by pushing forward the right lines of development. Whether that is by being an insider putting in five figures into a seed round in a useful startup, or by being a billionaire establishing a research foundation, you can move the needle. Early stage research is dirt cheap. Venture capital is overflowing the sandbags for any venture that can do something credible with its seed round. There are startups at various stages today that have means of repairing/removing some of the cell and tissue damage that causes aging, and are pushing towards human testing.
The game of life used to be limited. It used to have a line at the end, you are done. Everything in life and all of our culture is very much defined by the existence of that once-immutable endpoint. The endpoint is fading, however, in the sense that bringing aging under medical control is a research and development project that can and has been envisaged in some detail. But next to no-one has yet adapted to the new reality: the world is still full of old people playing the same old game of gathering points in politics and markets for some final score, and of young people aiming to be in the same position.
If there was sanity, the old game board would be thrown out, and immense interest and investment would be directed towards the biotechnologies of aging and longevity. There is a big difference between a world in which you can't buy time with money, and one in which you can.