Since you said capacity is fixed _at a given point in time_, this is technically true but not really useful.
Populating aging happens over time, not all at once. Overall production also changes over time. It’s not inherently true that for “non-producing” (not sure exactly how you’d define that) people to consume goods the “producing” people must consume less, at least not relative to past levels of consumption.
You're right, it's not necessarily true relative to past levels of consumption. But there's a limit to economic growth, and the choice of "paygo" vs "investment" probably only has marginal effects on the rate of economic growth, so the point stands.
"Non-producing" people are retirees (as well as children). People who don't produce market goods/services that make up the vast bulk of our material needs.
Populating aging happens over time, not all at once. Overall production also changes over time. It’s not inherently true that for “non-producing” (not sure exactly how you’d define that) people to consume goods the “producing” people must consume less, at least not relative to past levels of consumption.