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The grounds are then simply "tied off" inside the distro box, without any real ground connection. Interestingly, the typical outlet tester shows this combo as valid but I wonder about the safety!

If the tester is just one of the types with three neons connected across each permutation of the wires, this wouldn't be entirely unexpected. Neons draw only a tiny current, so it's likely the ones tied to the "floating" ground could have a sufficiently low-impedance path to glow via either capacitive coupling or leakage through the various equipment connected to the distro board.