The clickNotification was already set to None by way of the BasedOnDelta check in UICamera.ProcessTouch().
I didn't provide enough information in my original post. My problem ended up being we've been doing all of our button logic based on onPress events (playing a UI Sound on pressed, and doing button clicked logic on the !pressed).
After looking over the UICamera code I realized that we had been completely ignoring the onClick events. Up until now, it hadn't been an issue since we were just using simple buttons that were not draggable. Since onPress is always sent regardless of drag thresholds (as it should be), our buttons were always behaving as though they'd been clicked on when we released from a drag. I found two ways around my problem:
1. Add onClick UIEventListeners to my buttons, and move the 'clicked' logic out of the onPress handlers (which in retrospect looks like the correct way, and is how we should have set up buttons in the first place)
or
2. In my onPress code, check to make sure UICamera.currentTouch.clickNotification != UICamera.ClickNotifcation.None before doing my select logic (which is a bit more hacky, but perhaps more convenient in certain situations)
Anyway, just wanted to share my solution in case anyone else gets confused by this.