Interpolation, in machining terms, is generating a path that connects data points. Close to the ideal path, but constrained by the control limits.
The proper way to cut a circle is to ramp into the circle (using a smaller radius), cut 360 degrees at the proper radius, then ramp out (using a smaller radius).
This ensures that there is no overlap.
Unfortunately, it would take an EXTREMELY accurate machine to hold .0007 tolerance interpolating a bore. If the machine itself is accurate to .0002 positioning, you've already used up over half of your tolerance!
When you add in other factors such as tool wear and deflection, material hardness, temperature, etc., you're really pushing the limit.