They've had a secured network for years. It can operate on the same channel (but it would compete for signal) or a different one. It likely operates on a different one, but that doesn't mean it is free from interference. There are different ways of covering a wider area, and some involve placing different access points with different channels for the same SSID (i.e. the "DisneyParks" public network vs. the private network). And you've only got so many channels.
But I think the problem with the MDE/FP+ integration isn't so much the private network data (which is more likely over wired networks), but with even MORE increased guest usage in using the app to track and change FP+, which will generally increase awareness of the app itself for its other features, etc.
That said, if anyone can pull this off, Disney would be it.
This has, and will continue to be interesting to watch. They're writing a whole new rule book here.