I can do that tonight

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It's extremely common to lay hard-service cord across, well, almost any solid surface. We use YellowJackets when crossing driveways and the like, and try to stick to existing barriers (fence, wall, etc) and stay out of walking paths. Over grass, gravel, asphalt, sand- no one has ever questioned the placement.
I think this is more of a case that the NEC doesn't prohibit the practice so it's allowed. I also think that 590.3 and .4 in the 2020 edition are poorly written (and some of the others aren't much better).
BTW, 2011 and 2014 don't have a 590.4(C)(1); 2020 does but it's not relevant. This really looks like 590.4(H) territory (Protection from accidental damage).