Part of the Furniture
I'll meet you half way on this. I have multiple APs on my network. If my iPhone switches from one AP to another, it will change MAC & pull a new ip. (on my single network)
Same SSID? If so it is probably looking at SSID plus MAC of the AP (or some other parameter). My android keeps the same IP across the same SSID and two APs. But in your case it should only ever grab a few (however many APs you have) max I would think.
In Android it lets you enable or disable it per SSID I believe so that only works if it only looks at the SSID and nothing else. I guess apple is more aggressive, but that also means roaming will be more interruptive as it will lose its IP.