Unless the claimant filed a mineral patent application on or before September 30, 1994, then no, that is not the claim owner's property. That is still public land and the owner of that land is still the people of the United States. The claimant is not permitted to build any permanent structures on his or her unpatented mining claim and certainly is not permitted to turn the claim into a garbage dump. The only thing the claim owner actually owns is an exclusive license to extract minerals from public property, therefore any minerals that are extracted while the claim is active are also property of the claim owner (regardless of which party extracted those minerals and their legal authority to do so). This is why walking across somebody else's unpatented claim is not trespassing until the moment you get your pan dirty or pick up a rock and take it with you. If the claimant fails to pay the $155 annual renewal fee then the mineral rights go right back to the people, because that land never actually belonged to the claimant. They only own the license to extract the minerals. That license can and should be revoked if the claimant doesn't prove to be a responsible steward of the people's land.
Now if the claimant does in fact have a valid patent on the claim then yes, they do own the land, in which case unaffiliated parties would no longer have an automatic right to enter that land even just to pass through. Given that the claimant has owned the claim "for over 3 years" and not considerably longer than that, and given that the OP was present on the claim (obviously without permission from the claimant), it can be deduced that no, the claimant has not patented the claim therefore the claim is still public property and as such, the claimant's privilege to extract minerals there could readily be revoked.
This is my understanding. Please correct me if I'm wrong.
USC 30 § 26. Locators’ rights of possession and enjoyment The locators of all mining locations made on any mineral vein, lode, or ledge, situated on the public domain, their heirs and assigns, where no adverse claim existed on the 10th day of May 1872 so long as they comply with the laws of the United States, and with State, territorial, and local regulations not in conflict with the laws of the United States governing their possessory title, shall have the exclusive right of possession and enjoyment of all the surface included within the lines of their locations, -R.S. § 2322 derived from act May 10, 1872, ch. 152, § 3, 17 Stat. 91.
The mechanics of what happens to the “public land” once found to be mineral in character is expressly evidenced in the Organic Act of 1897, that “any public lands embraced within the limits of any forest reservation which. . . .” “...shall be found better adapted for mining or for agricultural purposes than for forest usage, may be restored to the public domain.” By private settlement under various land disposal laws of the United States, such as the Mining Law of 1872, “public land” is restored to the public domain. The federal agencies have management authority only over “ public land”, not privately settled public domain. The act of location, restores the land to public domain and the mining law provides the locator of such segregation “shall have the exclusive right of possession and enjoyment of all the surface included within the lines of their locations, -R.S. ァ2322 derived from act May 10, 1872, ch. 152, ァ3, 17 Stat. 91.”
Federal mining claims are "private property" Freese v. United States, 639 F.2d 754, 757, 226 Ct.Cl. 252 cert. denied, 454 U.S. 827, 102 S.Ct. 119, 70 L.Ed.2d 10 3 (1981); Oil Shale Corp. v. Morton, 370 F. Supp. 108, 124 (D.Colo. 1973).
“but so long as he complies with the provisions of the mining laws his possessory right, for all practical purposes of ownership, is as good as though secured by patent." Wilbur v. U.S. ex rel. Krushnic, 1930, 50 S.Ct. 103, 280 U.S. 306, 74 L.Ed. 445.
Mineral deposit claims and the property thereon and livelihood therefrom may not be tampered with, or denied protection of government which property and livelihood shall not suffer impairment or interference. Setting the required boundaries of a mining claim literally sets a boundary describing land separate and distinct from agency authority placing the claim under the exclusive authority and jurisdiction of the locator. And this interest is stated, as case law and Forest Service Manual details, at: FSM 2813 - RIGHTS AND OBLIGATIONS OF CLAIMANTS; 2813.1 - Rights of Claimants
By location and entry, in compliance with the 1872 act, a claimant acquires certain rights against other citizens and against the United States (FSM 2811). By clear and identical language, Congress has stated in the Organic Act of June 4, 1897, the Eastern Forests (Week’s) Act of 1911, and the Taylor Grazing Act of 1934, that there was no intention to retain federal jurisdiction over private interests within national forests. The courts have consistently upheld the ruling in Kansas v. Colorado since 1907.
The rights the locator maintains exclusive possession even against the government, including all agencies, must be preserved, “saved”, in every land disposal act subsequent to the original granting act of 1866, including the FLPMA. Those rights include that the locator of a valuable mineral deposit, “shall have the exclusive right of possession and enjoyment of all the surface included within the lines of their locations.” The courts declared possessory title in 1864 before the grant itself. This grant is exclusive conveying permanent, title, as good as patent, such that the title shall not be affected by the paramount or trust title of the United Stated, referencing 30 USC 53, that “No possessory action between persons, in any court of the United States, for the recovery of any mining title, or for damages to any such title, shall be affected by the fact that the paramount title to the land in which such mines lie is in the United States; but each case shall be adjudged by the law of possession”. The existence of valid existing rights by relation back of the granting act of July 26, 1866 disposing the uncommon mineral estate held in trust are required to be “saved” in subsequent acts as a “specific use” of the public domain to the Locator. This mineral estate is treated like any other granted property, the contract of which a grantor in this case Congress, or by agency, treated as a mere proprietor may not breach.
It must be noted, referring to the italicized emphasis in both Section 22 and 26 above, that the former referencing “regulations prescribed” and the latter the “the laws of the United States...”“and local regulations” are only those laws and regulations relevant and “governing their possessory title”. This was a miner's law for miners. The only “regulation authority” retained by the federal government, was that oversight authority in dutifully disposing the soil pursuant to the various grants, to avoid such things as fraudulent public land entry, not to regulate the uses thereby those disposal acts.