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Fingerboards are too often unevenly sanded with a bit of fall-off right where they contact the nut, so about the LAST thing I would consider is actually measuring string height at that position.
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That is my take on it, as well.
The only time I would even consider it is when I personally have leveled the fingerboard, but the 'eyeball' method works just fine.
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So you see my dilemma: I cannot shave the shim down while the strings are under tension.
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I don't recall a time when checking the nut height on an unstrung guitar using a thin straightedge gave a false reading, but most of the guitars I work on are older, and have thick necks that are pretty rigid. In other words, they don't move a whole lot when going from strung to unstrung. To tell the truth, I still don't understand why some neck movement would be a problem...unless the straightedge being used to check it was way longer than necessary. After all, if neck movement gives a false nut height, it will also give a false first fret height.
The one exception to this is when the slots are vee-shaped, rather than round- or square-bottomed. In that case, the string will actually be higher than the bottom of the slot, as checked with the thin straightedge. But that is easily remedied with rounded nut slot files. IMHO, vee-shaped slots are a bad idea, since they are susceptible to string binding during tuning.
The thin straightedge I use for checking nut slot height is nothing more than the back edge of a thin razor saw blade. The kerf is about 0.012", and the body of the blade is 0.010" thick. I use the same blade to cut 'test' slots in the middle of the string slot, as a gauge for the action. My procedure for cutting nut slots is simple....saw the thin test slot until it is level with the tops of the frets. Height of this slot is checked with the back of the razor saw blade, by simply flipping it over. Once the test slot is done, I go back and widen the slot with a nut file, until the test slot disappears. Voila....the slot is done....without ever checking the height with a string.