I found a Willie Rath, age 14 yrs. on the 1880 census in Brown County, Kansas. Parents listed as Alexander and & Emma Rath. I could not find him in Jewel County, Kansas on any subsequent censuses. No Rath's in NM. Not sure how they came to be buried out at Acme because it is a "family" cemetery for the Bivens and their kin. I would suggest writing the person who posted the burial info to begin with and see where they came by it.
I will try and check the County Clerk's death records and see if I can find anything.