Sorry it's taken me so long to reply, PaulBC. I thought maybe I'd get an email notification when someone had replied to my post, so I wasn't aware that there had been replies already until just now! There's probably some way to set up notifications, I just haven't looked into the settings yet. Anyway, here's a patent that refers to the valve mechanism that's used in your daughter's disposable set.
http://www.google.com/patents/US5088515. It's not very easy to read by a layperson, but the abstract and the body of it describes that the flexible membrane seals off the mouth of the valves using air pressure. As for costs, I don't know what it costs to make the solutions, but they have to be sterilized, which makes it more expensive than something like Gatorade. Thanks for the suggestions for device improvements!