>Extremely naive question, but I always wonder how you can "bootstrap" this kind of precision — intuitively for something to be this precise, the tools and equipment that "create" it should also have to be more or less equally precise.

You can build a machine like that and most machines are built like that because simply reproducing the precision that is already in the machine is cheaper than building a complex intelligent system that knows how to compensate for flaws in precision. Think about how many 3d printers do auto leveling in software rather than simply make the bed perpendicular to the print head by hand. Those old manual milling machines and lathes didn't have all that fancy software so they simply reproduced their own flaws.

Well, given a smart enough human he can compensate for the flaws in the tools and get to a higher degree of precision.