Hi David,
So the NetDispenser's default configuration is WiFi-to-WiFi, and it would connect to that same DNS server as would any student phone. You, or anyone, would not need special accommodation by the IT department.
In a home-use scenario the parent would just lock the kids out of the main home router (via the config panel broadcast by the router) so that they can only connect through the ND. That's as easy as not telling them the password to the home router.
In a school-use scenario, without any accommodations by the IT dept, they could connect directly to the schools WiFi, or through the ND, which is also connected to the school's WiFi. The ND is a pass-through device, aka a WiFi repeater. It's a middle-man but you don't need special permission from IT to use it, it would just show-up as an additional access point. So the "reward" of internet access gets nullified as they can just connect as before and they're online. The simplest solution is just to appeal to students to "play along" and do it your way, i.e. through the ND.
This may sound a bit totalitarian to some people, i.e. restrictions, denial of access to information, etc ... so perhaps it's worth recalling the original use-case, which was to periodically supplement video games and internet surfing with something educational. And to remember that it can be turned on/off anytime the parent (teacher) likes, so that it only serves as a tool when you want to use it. Some might choose to leave it on always, as I did, others might not. But it's not about totalitarianism so much as just "read this article first, before you dive back into video game land, or whatever".
I'm still planning to make a reusable presentation in the next couple days, and will address this there. It's a good question, for sure, and the real answer is that the ND was developed primarily for home use, but we frequently find ourselves discussing in a school context and this is an issue that we have yet to totally work out.
-Charlie