That makes no sense. What a small base sizing die does is actually reduce the base of the cartridge, just above the extractor groove, to a little below specs, I think by .001 or .002. It changes nothing in the nect or the shoulder.
Since this is most likely your problem with the once-fired mil ammo, that may, repeat may, help you.
Now for bolt rifles, it will do the exact same thing. In fact, I use a small base die for my F-TR .308 rifle, because the chamber is very tight. So, when I resize it, there is very little work being done, it's more like a touch up and the ammo slips into the chamber prefectly, but without play.
For the vast majority of sizing operation, you do not need a small base die, I only use it for my two match rifles. Everything else gets a regular die, but I never mix the brass.
Some people believe it is better to simply neck size the bolt action ammo and bump the shoulder back a bit. They think they are getting more consistancy that way.
They are wrong.
At some point, the use a body die or an F/L sizing die "when the bolt gets difficult to lift." What they fail to understand is that the case has been changing with every firing and then they change it once again, big time, with the body or F/L die use. The next firing will be very different and they also overworked the brass stuffing it back.
By F/L sizing every time, one gets a consistent cartridge every time and if properly adjusted and with the use of bushing dies without the expander ball, the brass gets worked very little.
I would love to see where they recommend against using a small base die for a bolt action. I will say that in just about every case, it's not required, but it will not hurt anything to use one.