I see there are several comments above about broken links to the source data set. It looks like the source data would be the CPW Administrative Boundary Data which is available here.
You haven’t been clear about which layer you’d be using but it appears it would be the CPW Public Access Properties layer.
The thing about boundaries is that they’re not easily verifiable on the ground. It really doesn’t matter whether you’ve camped there. You’re not going to correct them by hand, and neither is anyone else.
It does matter whether the boundaries get imported at the right locations in OSM, and properly transforming the data is necessary to get that right. It can see that the default transformation in ogr2ogr is just reprojecting the coordinates onto a new ellipsoid. It’s not actually applying any grid shifts. Do it right, and the coordinates will be transformed with an error of much less than 1 m.
If you care about this stuff, you do care about doing it right, don’t you?