To me runout (per ANSI/ASME Standard Y14.5M 1994 and later) is any/all variation that can be measured by turning. So it depends on what direction and the location of the dial indicator as to what's being measured. It includes all sources, variation in surface, holding devices and bearings. Therefore it is an incredibly usefull tool to use as it is easily done, but it's limitations are that it includes all sources of variation.
To specify something that runout esitimates, one could specify:
roundness (circularity) where all points are equadistant about a point;
cylindricity, where all points are equadistant about an axis; or
perhaps coaxiality wherein the two axes in question coincide.
The problem of measuring those is that one has to make many measurements and calculations taking 30 to 40 minutes for each set done. Obviously enough reason to use runout unless you're getting paid cost plus.
So the issue is in measuring runout two fold. One the location and direction of the measurements and two, the devices (and the error introduced by them) used to hold the bullets.
This is why we have fixtures, with very precise bearings, for holding round elements for measuring - to avoid the error caused from the wear on the production equipment bearings.
One can devise all kinds of fixtures for measuring runout which can, if designed right, be indicative the bullet being out of round or when loaded whether or not it is reasonably aligned with the axis of the bore. If the design is right it will have the same measurement as roundess or coaxiality PLUS the error of the bearings and fixturing.