It would be surprising if any, let alone an amateur market, three jaw chuck holds work absolutely true.
Even collets are not infallible, unless direct in the mandrel / quill taper. And that assumes that the taper bore has no eccentricity relative to the bearing surfaces!
If you want to start talking REAL tenths of a thou, or better, you are going into the realms of Standards Room conditions with CLOSELY controlled temperature and humidity.
There won't be many of us with those sorts of environmental controls!
If you want the workpiece to run absolutely true, use a four jaw and adjust until the DTI shows Zero eccentricity.
Allow plenty of time for this.
A good Industrial grade three jaw chuck will probably not do much better than 0.005" (0.127mm) total eccentricity. And to complicate matters, it will probably alter as the diameter changes.
(I know of one venerable three jaw, not mine thank goodness, which has an eccentricity of 0.036", but still being used to produce good work!)
Eccentricity in a three jaw is only a problem in second operation work. If you do all the turning / milling without moving the workpiece, the machined diameters will all be on the same centreline. Once you take the job out, you have to centre it up in a four jaw for subsequent work.
Howard