building a road is not corner jumping. Logic would say the argument that you "crossed" private land also means you stayed on public land. the main "gotcha" here is how accurate is a GPS?
I find it wrong that public land can be landlocked by private land, there should be some right of way required. However that also goes against public land rights, so it's a catch-22.
I was in WY in October and we looked at a house for sale. It was on a dead end road and all the land behind it and the other houses was public. We chatted with a house owner and asked about a 2 foot gap between his fence and the property we looked at. He said since it was all public, they agreed to leave that gap for people to walk in. It wasn't wide enough for an ATV, heck even a horse would have had a tough time, but you could easily walk it. Then again there really was no place to park, but at least there was access.