Pragmatic Metrology - Surface Plate Basics - Part 1M 

8+ months late for a possible answer to your question, but highly doubtful any height gauge could be used as an actual squareness comparator. One reason those designated squareness comparators are so expensive is the materials and design that goes into making them. Most I know of use basically a fairly thick but narrow granite surface plate inside them as the true surface for the gauge travel. Even then they still have to be calibrated to a known reference surface like your cylinder square with the 3 fine thread adjustment screws on there base. While my digital twin beam Mit height gauge is I think very well made, it does drift enough to make an accurate measurement difference over the full travel when checking against my cylindrical square. These height gauges would be built to be very close to a true 90 degrees when placed on something like a surface plate, but in my opinion, those actual comparator's are no doubt an order of magnitude better. I looked at a few different types of height gauges before buying my 192-630-10 trying to save some money. And if you check the specifications for there repeatability and accuracy, that $1500+ price level is about where they start getting fairly accurate. Anything under that will have guaranteed repeatability numbers of only being repeatable to within a couple of thou. Since these height gauges all have defined accuracy limits, there would be no requirement of building them any more accurate or square over there vertical travel than they are. The other issue is there has to be at least some clearance for the height gauges measurement head to move up and down the column, and a certain amount of variable flex on the single or dual columns due to gravity and where the head is positioned on the column. Again that's much less accurate than the way those comparator's are designed and built.

So that would mean he accidentally and coincidentally achieved “0”?