Being "about" health doesn't make it health. If I have a magical machine that produces an infinite number of bleggs, I can describe the state of bleggs as being infinite, but I still can't describe blegg machines as being in infinite number.

It matters. You're arguing that healthcare isn't a finite resource because allocation of healthcare could conceivably produce a non-finite amount of health. But it doesn't follow from that that healthcare is a non-finite resource. If we only have one Perfect Health Machine, a theoretical machine which enables clinical immortality, we -still- have to decide who gets to use it. If we decide to build another, that consumes finite resources. We can only have a finite number of Perfect Health Machines which can each only process a finite number of people in any finite amount of time. The potential for "infinite health", however one defines that, doesn't imply a potential for infinite healthcare.