Ah yes, I suppose it doesn't bother putting the TextField in Starling's native overlay when it can't be edited. I probably should have added it anyway, when it is still supposed to be selectable.
It's looking like e.preventDefaults() might be the way to stop the keyboard appearing but this requires a flash.event.
The event to listen for would be
SoftKeyboardEvent.SOFT_KEYBOARD_ACTIVATING, which can be cancelled. You should be able to listen on the native stage because it bubbles.