Ohio farms, I did a followup with ODNR, and it seems we are both wrong! What matters is where the deer was shot. If I hit it on my property, my landowner tag is all I need to reclaim it from someone else's land, as long as I have WRITTEN right to pursue from that landowner. I am to keep my weapons with me as I may have to put it down once I find it.
The only real difference between a good tracker and a bad tracker is observation. All the same data is present for both. The rest is understanding what you are seeing.