Most of the less expensive commercial brass is less precise than, say, Norma, which is excellent. I have measured up to 9 mils (0.009") of web thickness variation in WW .308 brass using NECO's gage system, which let's you measure case wall thicknesses quite literally inside and out (
www.neconos.com). My Norma 6.5-284 brass has never shown more than 1 mil of runnout on this gage; but then I paid almost 70 cents apiece for it.
Runout in the sizing die could render your casehead out of square, if it is angularly off axis, or, if it is a parallel axial offset, cause no case problem at all since the shell holder will usually let the case slip a little off axis as needed.
Having said that, it assumes the problem is with the brass. It probably isn't. You referred to runnout, but if what you measured is runout of a loaded cartridge at the neck/brass junction on a runout gage (bullet tilt runout), then the problem is almost certainly your seating die and not the brass or the sizing die.
I loaded 30-06 using both RCBS and Redding standard die sets for a couple of years in the 80's. Both assembled cartridges with bullet tilt runout of up to 8 mils. I then bought a Redding Competition Seater die. No cartridge runout ever measured greater than 2 mils after that, and those that did invariably proved to have case necks 2 mils thicker on one side than the other (this was mostly Lake City military brass back then). My dad acquired an RCBS side-loading precision seating die at the same time, but my Redding always beat it by almost 2:1 in precision. I've been buying and using the Redding competition seaters for all rifle calibers ever since.
Nick