That's mostly right, but as with a lot of these kinds of things, it's more complicated than that. Some of these checkerboard patterns were caused by systematic deforestation to help build the early railroads, but the checkerboard pattern itself comes from the way the federal government subdivided and sold Native American land to private individuals. It all goes back to the Dawes Act and our exploitation of indigenous tribes.

From a 2012 Democracy Now interview:

Eastern Navajo has a lot of—what we call the checkerboard area, and there’s these individual Indian allotments, which were created through the Dawes Act. And because of this individual ownership, Navajo allottees, they have the right to lease their land. And so, what the company does is they target individuals in our community, and they really, you know, use this divide-and-conquer tactic. And what they’re doing is basically promising all these riches and basically monetary gain for an already poor community that doesn’t even—a lot of our people don’t even have running water or electricity. And so, some of the individuals are dependent on this—on these promises of a false economy and jobs and all these good things that they—that they say they’re going to do.

It has caused a lot of problems for the tribes and their sovereignty.

Beginning with the Dawes Act of 1887, Native Americans, including the Navajo, were assigned plots of reservation land on which to practice subsistence farming. This was an attempt to assimilate Native Americans into Western European land use and domestication practices.

The checkerboard mix of lands owned by tribes, trust lands, fee lands, and privately-owned tracts severely impedes on the Navajo nation's ability to farm, ranch, or utilize the land for other economic purposes. Problems of mixed jurisdiction (tribal, federal, state, or county) have also contributed to economic instability, as well as to racial tensions and community conflicts. Source