A couple of quick points that may help someone avoid problems in the checkerboard. Anadarko (formerly Union Pacific Resources - the land ownership subsidiary of the railroad) usually includes surface access control in thier surface use leases - the lessee, (the ranch including the leased land), has the right to control access. Some allow access, many do not. The checkerboard around Rock Springs as far east as the Continental Divide is owned/leased by Rock Springs Grazing Association, which has never required permission to access the deeded lands, but obviously could if they wanted to. It's nice to have such a large landowner that allows public access.
And a quick note on corner crossing. No matter what you read on the internet machine, bottom line is that it is not legal to access public lands via corner crossing in Wyoming. You can feel free to do it and take your chances, but if a landowner wants the county Sheriff to prosecute, they will, that's their job.