I was going to ask how the heck a railroad works across a checker board but googling railroad land grants checkerboard explains it. Googling flathead national forest “land grants” got me this (PDF), which says:
The forested landscape of the Swan Valley is a checkerboard pattern of public and private ownership, a remnant of Federal land grants to railroads over 140 years ago. The majority of private land it held by PCTC, which acquired the land from the railroad in 1989, and has managed its holdings as an industrial forest.
I’m only assuming that’s the same place, since Swan Lake is just north of the checkerboard on the map, but for all I know, it could be another Swan Lake in a different state. Just scanning the pdf, I didn’t see anything to positively ID the location.