I have CS2, which is older as well. I have a full backup of the whole suite on my external hard drive, so I don't have to keep downloading the software every time I upgrade to a new computer.
As far as not really owning the software we paid for, it's been something that's been around for quite a while, though not necessarily in the public view, so to speak, so folks are now finding it "new" thinking. Unfortunately, we're just paying for the "use" of a product, and not the product itself. The only time you own something outright, is when you can actually take it home with you, but in the instance of software, you're just getting a "copy" of it, not the only copy of the software in existence.