I have heard this many times. However, in all of the books I have read and studied, I cannot find the evidence to give credence to this myth, only evidence that it is just that, a myth perpetuated by the uninformed.
Both rounds start life with the exact same dimensions. Check it, I have using unfired rounds. However; when fired in a mil spec chamber, the brass is larger than when fired in a SAAMI spec chamber. A military firearm has a much looser chamber tolerance than does a SAAMI-spec'd chamber. No surprise there...
I understand by my own research and experimentation, that the problem falls, not in using military brass to reload, but using civilian brass in a military firearm. Since the chamber is larger, it needs more brass to fill it. Therefore, the heavier, thicker brass allows it to flow and stretch to fit this chamber whereas the thinner commercial brass could fail to do so and would rupture.
This led me to believe that an unsized once-fired commercial brass case that has been reloaded would easily chamber and fire in a military chamber. Having been blessed with a close relationship with an FN, I was able to test this theory many years ago. The unsized commercial reloaded cartridge chambered and fired just fine in the FN. The reverse cannot be said. The case is too long and will not allow the action of a SAAMI chamber to close and lock.
As long as you resize your brass back to SAAMI specs (which all F/L .308Win dies do) you will not experience any problems with feeding or firing. However, you are working your brass a lot which shortens case life, but that's how semi's go...live with it.
Enjoy...