it would have put a big hole in my (and, frankly, Karl Popper's) exposition of science as being all about demonstrability and falsifiability...
I disagree, I think it's a great example. Here is a pure theory, it's got ideas that are mostly untestable. Astrophysics and particle physics are at the bleeding edge of our learning, and have many facets which are untestable. We're working toward ways of testing many of these things, but until we do, it's still theoretical if it hasn't been tested. We've never sent a probe to the edge of a black hole and observed what it's like, we can only theorize that a black hole exists because of the x-ray radiation emitted near its event horizon. We can observe with a spectrometer that the universe is expanding, but can only guess as to why or when the expansion started.
It's very important to understand that some theories are more theoretical than others, and this is the root of what science is about. A discussion like this is a great example. You can't put finite vs. infinite universe theories into the same boat as things that are testable like elementary biology. They're both science, and they both can be proven wrong and thrown out if we find evidence which contradicts the theory, it's just that one of them's got a lot more evidence backing it up than the other.