Jim the standard is not "significant disruption of the ground" the agency standard is "significant disturbance of surface resources". Words really do matter.
The ground, as you call it, is where the minerals the claimant owns are found. Locatable minerals are subsurface resources owned by the claimant, not the federal government. You have every right to dig, disturb and remove the minerals even if the subsurface disturbance is significant because minerals are not surface resources. The surface resources are not owned by the claimant, they are owned by the federal government (on claims located since 1955).
Surface resources are those things the federal government can sell or are required by law to protect. Things like timber, salable minerals, free flowing streams and endangered plants or animals. This is where the federal agencies have power over the specific methods of mining used in a specific location. They only have that power IF the mining could cause significant disturbance of surface resources. If your mining will not significantly disturb surface resources the BLM has no choice but to allow your mining without a Plan of Operation.
By law the federal surface management agencies have a duty to protect the surface resources from "unnecessary or undue degradation". If the mining causes significant surface disturbance but the disturbance is necessary and not undue by industry standards the mining can proceed despite the significant surface disturbance.
In mining unnecessary and undue degradation is caused by not following industry "Best Practices" or from poor planning. The unnecessary and undue degradation standard is only applied to the surface resources. The subsurface minerals and your methods of extracting them are only governed by federal and state mine worker safety standards - not the BLM or Forest Service.
I just looked and there are three operations using backhoes on their mining claims on BLM managed lands within an hour drive of me. Those miners are all digging under a notice to the BLM. With the notice system the miner notifies the BLM of their intent to dig their minerals and their plan to meet the Best Mining Practices standards. The BLM has 15 days to request more details, suggest changes, request a plan or allow the digging. If the BLM doesn't reply in 15 days the miner can proceed without further delay. In either case no permit is needed or issued. The Notice is a case action on your mining claim case file - sometimes a small reclamation bond is requested which will also be noted on your case file. This system has been in place since 1980. The law and regulations are the same for federal lands no matter which state you are mining in.
As far as someone using a diamond saw on a rock on public lands - that's illegal without a permit. Rocks are not locatable minerals. If you want to cut and remove part of a rock from the public lands that would require a permit or a lease the same as sand and gravel, acorns, mushrooms or taking or harvesting any other surface resource. Often these permits are given for free or very little money. While I have no personal objection to what they did I'm not surprised they got a ticket.
I hope that clears things up Jim. It was a good question. I think it's important for miners and prospectors to understand the distinctions between their rights and responsibilities and those of the surface management agencies.
Heavy Pans