I think this is an EXCELLENT local rule in spite of any possible "violation" of USGA rules.
There are two ways for this problem to be solved in compliance with the USGA rules of golf. First, a tree, a wall of trees or other obstructing growth (e.g. the "Hinkle tree"). Second, a large fence at one side of the tee box.
Those who view the USGA rules of golf as their own versions of statements from the Vatican would prefer this course to spend extra money (and therefore make this course more expensive to play, when this course appears to be intended for the lower end of the price market), and/or to add a very ugly artificial obstruction.
Instead, the locals have come-up with their own "gentleman's agreement"/local rule, without concerning themselves with the USGA's opinion of this matter (I doubt many at this course are preparing to qualify for the U.S. Open).
They have created a rule that implies that all agree to pretend that something is blocking their ability to hit over another green, and therefore must play the lay-up. And why did they create this clever artificiality, so as to protect the safety of others on this course. And to really make sure that this "gentleman's agreement" is fully complied, they have instituted the maximum penalty to expressly show their seriousness about this matter. GO THE ROUTE OVER THE OTHER HOLE, AND YOU MUST RE-TEE, COUNT THE FIRST SHOT, AND ADD A PENALTY SHOT.
If one abides with this “gentleman’s agreement” and plays the lay-up, no USGA rule is explicitly violated. Only those unwilling to abide with a local rule whose sole function is the safety of others, and then add the penalty strokes appear to be involved with the course in some violation of USGA rules.
I suppose the rule could have instead been: go over the other hole and the shot must be re-played with no penalty (i.e. like some local rules that allow a shot that hits overhanging wires to be re-played). But perhaps they wanted to be sure some did not try to play to close to the elbow, knowing a stray shot could just be re-played, but still leaving those on the other hole at risk.
But to reiterate my primary point, the people actually involved in this situation seem to have made a good decision, without limiting themselves to the commandments of those far away and not intimate with this place or these people.