No one goes in or out of that airspace without the US/Australian military knowing about it, and if you do, there is a real possibility of the Australians shooting you down. You will at least be forced to land and most likely be arrested.
That does not surprise me at all.
I lived in NM for many years and traveled Southern NM and South Eastern AZ. Had lots of friends at the Labs. Ham friends of mine mostly, some MARS types. I ran a Navy MARS station for 20 years.
There were several no-fly zones around White Sand and Alamogordo. They have been that way since WWII.
Lots of other strange critters in the desert too.