The wild part here is that nobody in the 1860s "planned" this fight, but the incentives of that railroad grant scheme basically created a privatization hack that took 150 years to fully mature.
Checkerboard grants were sold as a compromise: give half to the railroad so they'll build, keep half so the public can "share in the upside" later. In practice, the private squares became de facto gatekeepers to the public ones, and once land got valuable enough (ranching, minerals, hunting rights, viewsheds), the optimal move for the private owner was to weaponize ambiguity in trespass law to extend control across the whole block.
Corner crossing is interesting because it attacks that hack at the most abstract layer: not fences, not roads, but the geometry of how you move through 3D space above a property line. If the court says "yes, you can legally teleport diagonally from public to public," a ton of latent "shadow enclosure" disappears overnight. If it says "no," it quietly ratifies a business model where you buy 50% of a checkerboard and effectively own 100%.
This is why the case drew such disproportionate firepower: it's not about four hunters and one elk mountain, it's about whether "public land" means you can actually go there, or just that it exists on a map while access gets gradually paywalled by whoever can afford the surrounding squares.