There definitely was a lot of math involved in the history of the section monuments out there, just as you suspected. The section corner to the north of that 1/16th monument was reset in the late 80s by double proportion, and for unknown reasons that 1/16 monument was set at the same time, despite having no apparent relevance to the property being surveyed at the time. Clearly the fence isn't remotely straight, so I don't know that arguing that the fence was intended to be built on the line of an aliquot part would do any good either. I believe the argument was purely AP and included testimony from previous owners in that area that the fence was assumed to be the property boundary.
As for financial motivation for the AP, there is an irrigation ditch in the disputed area. Water is gold.
That typically happens, a double prorate is used to control 1/16th lines and of course it seldom fits perfectly. Ditches work differently there it seems, here it's irrelevant who's property they are on, everyone gets access to a ditch if they have water rights attached to it.
Not all fences are intended to follow boundaries. That fence not being very straight makes me think that it was intended merely to "turn the stock" rather than to mark any claim of right. I have doubts that it would bear up to an AP claim. The burden of proof is on the claimant to show that the fence was intended to follow the claimed boundary. A simple denial would likely be sufficient to defeat an assertion that it was.
As others have noted, the provided map gives us no clue about the value of the claimed markers. Found or set and from what evidence?
In the 3 states I am licensed in the basic requirements of AP - exclusive, hostile, continuous, etc., etc. - are similar if not identical (notwithstanding Oregon's "statutory AP" version, which makes successful AP claims post-1989 very rare) . But the nuances as to what actions constitute these elements vary.
For the record...I found very few examples of AP in the Oklahoma court decisions. The OK court greatly prefers practical locations.
Doesn't dispute the survey but claims to the old fence? That's a dispute my friend. My experience is when encountering conditions like this it usually isn't AP or an encroachment. Usually acquiescence but not always. Can't tell which without more facts.
A thing to consider in AP cases is trespass. AP happens the moment the statutory time period is met. The judge ruling in favor of the adverse possessor is essentially ruling that said person has owned the land in question since the all the requirements of AP were met. I've been involved in one AP situation where my client (not a nice guy) was sure he already owned the property by AP. If the situation had been reversed, and I was surveying for the abutter, the AP landowner would likely have sued me for trespass and/or damages if I'd cut anything on the property he was claiming. I'm not sure how that would play out in court since there's an obvious gray area, but if a neighbor is telling your crew to get off his property, you may want to listen even if you know a judge has yet to formalize the adverse possession.
