If the rifle has a tight chamber, that 0.002" can be enough.
Even the "old standby" LE Wilson cartridge headspace gauge may not catch this, as those gauges are reamed deliberately oversized in diameter to make sure there isn't any interference with measuring base-shoulder. (And the neck hole is also oversized.)
Another thing that can occur is an "out of round" chamber. Unless the case is aligned with the axes of the ellipse, it may appear to be tight just because it isn't round. If there is a "shiny spot" on the side of the case, this could be the out of round chamber fighting the case.
If you have the patience, you could try inserting a fired (not resized) case using different orientations and see if there is a difference. Ideally, there won't be.
.30-06 Springfield: 100 yrs + and still going strong