Those appear to be markers from a US Veteran’s cemetery. They are, indeed, US Gov’t Property.
http://www.cem.va.gov/hm_hm.asp
It appears from the story that the original tombstones were replaced with new ones, and the original ones were disposed of, apparently by dumping them on this property decades ago.
I’m not sure if the property back then was a legal dump or if they were dumped illegally on private property. But, as I understand it, once you throw something away you give up and property rights to the item. If the government threw the old headstones away (as seems to be the case here), then the current property owner may be able to claim ownership.
These things are probably pretty valuable as a collector’s item. I doubt military tombstones come on the market often (at least not legally).