You can machine anything to any tolerance, assuming that you can measure it (and you have enough time.) In other words, you can create these tiny parts using relatively crude tools. (Files, saws, lapping, grinding) The critical part is being able to measure the part you are making, so you know if it is good enough or if you need to take off more material. In a 500 year old clock, the parts would have been made to only fit in that clock. Every part would be slowly made by test fitting it against the part it rides against. The fitment would be judged by feel, or by using blue die to see where two surfaces were touching.

Using modern measurement tools, you can machine to pretty tight tolerances, even if your lathe/mill is extremely worn.