The Cross was there waaaaaay before the "The Mojave Preserve" was!! The Preserve is a Bill Clinton invention. First the famous "Mojave Phone Booth", now this!
See: http://www.deuceofclubs.com/moj/mojave.htm
for Mojave Phone Booth info.
Also this:
http://www.geocaching.com/seek/cache_details.aspx?ID=2273
It was under the BLM's jurisdiction before that, and was evidently a sore spot with the environmentalists. Apparently the BLM was granted the land immediately after new territory was aquired from Mexico, but this is murky in what I've been able to find.