It's just a document, suggesting a path forward, but does not have buy-in from anyone, and the existing space treaties we have establish everything off-world as "community property".
I ask because the Chinese are pretty close to putting a man on the Moon.
I expect the next people on the Moon, despite their nationality, will at least make an attempt to visit one or more of the sites where people have already been, for many reasons: to validate their achievement, to debunk the Moon landing doubters, and just because HOLY SHIT I AM ON THE MOON AND THIS IS MY BOOT IN BUZZ ALDRIN'S FOOTPRINT!!!!
Further, on Mars, I fully expect some scientists are going to be tasked with doing autopsies on failed missions. Photographing impact craters and debris fields. Visiting hardware that crapped out for an unknown reason (Spirit?), etc.
Just approaching these sites will alter their forensic and historical value.
Footprints around the grass at Stonehenge are gone the next day.
Footprints on the Moon and Mars are there for the lifetime of whole civilizations...