Okay, I know what is going on here.
Our WAPs have their own management VLAN and each wireless network has it's own VLAN. These all connect to a single physical network interface on our firewall, so I did a bunch of testing by adding ACL rules to block access to the internet, DNS, and/or the gateway.
The Ruckus Unleashed WAPs do a bunch of checks. You can see this with the "show internet" command on the CLI. The system does a check against the gateway, DNS, and the internet-check.
To get the Unleashed WAPs to freak out and reboot, they need to (fail the gateway check) AND (fail the DNS check) AND (either have internet-check disabled OR fail the internet-check).
The reason I noticed this strange behavior was that our gateway was a firewall which was not allowing ping. This was dumb default from the firewall which I had not previously noticed, and I ultimately changed it to allow the Ruckus WAPs to ping their gateway.
Even though the Unleashed instance was previously failing it's gateway check it was happy to continue working as long as the internet-check was succeeding. However, when the internet went down, both the DNS check and the internet check was failing, causing the WAPs to all reboot.
So, the situation isn't as bad as I originally thought it was, but the question still remains... why does this this behavior exist at all?
Theoretically many (even most) small businesses are going to have their WAPs on the same layer-3 network where they might have file servers, printers, and other local network resources. The DHCP server might also be on the same network, separate from the firewall/router. If the firewall/router goes down for some reason, it seems harmful to then also artificially induce an otherwise-unnecessary wireless LAN outage by rebooting the WAPs as well.
I think it's especially ridiculous that the Unleashed instance can fail it's Gateway and Internet check and yet if the DNS check succeeds it's fine. Gomer Pile says "That don't make no sense."