While you have identified a few of the simple things involved in machine tool accuracy (balls screw quality, minimum command resolution, minimum step response, bearing quality) there is a whole lot more involved in machine accuracy.
Things like machine base size (the structure bends and deflects as the tables move and as cutting take place.
Spacing and placement of the ways which affect how square of a structure you can build.
Thermal expansion differences in parts as spindle housings and ballscrews heat up during use.
Dynamic stiffness of the spindle and tool joint connection when cutting from opposite directions and about a hundred other things that you only learn after 30 years of designing machines.
Assuming the machine has adequate resolution you just need repeatability to make tight tolerance parts. You cut oversize then bring the part into size by tweaking the code and/or tool offsets.
If you want to put a part on the machine and run code straight from the model and hold a thou. you need to add at least one zero to your price range.
You will need a very stiff machine, HSK tooling, a built in automatic tool measuring device (the tolerance on the cutting tool will eat up your thou all by itself), linear scales and a measuring probe. If you were willing to live with very light finishing cuts (read very slow cycles) you could pull this off for about a quarter million or so.
You are correct in that you need a machine that repeatably position to .0001 if you want to hold .001 but you don't need accuracy better than .005 as you adjust the machine to the correct part size.
A good machinist can hold .001 on a worn out B-port with .050 backlash in the acme screws that are only accurate to .005, worn out old bearings on the screw ends, and .010 squareness error in the table.
Bob
You can always spot the pioneers -- They're the ones with the arrows in their backs.