My google-fu indicates it is a water right claim that was granted or claimed improperly. In States with Prior Appropriation laws, someone makes a claim and it is recognized by the governing body; but later shown to be false.
e.g.
Nestle false water right
Also a bit more context might help. From your second posts it appears you are listing Irrigation Water rights and ditches. Both would be false due to the State (and many other western States) policy of prior appropriation. The "I got here first" rule for water use. Irrigation Rights would be false, if you did not have specific rights deeded to the property by people from very long ago. (My great great great Granddaddy used to run
cattle all over this range, so he was given water rights in 1850!) The same with ditches. Since water rights do not matter where the water is or flows, the ditch, stream or river that flows through your land would be a false right, because someone downstream (or up) has already a valid claim to it from a prior date.
A not so great way to manage water, but these precedents are still on the
books from the foundation of the territories.