Got a very nice .450-.400 3"(thick rim) in and the guy is concerned about primers backing out upon firing the Hornady ammo.This is a modern three bite action solid as a rock,no headspace problems,the firing pins are not bushed.Primers are backing out .004" to .005",no ignition problems, is this cause for concern?Any help would be greatly appreciated.

hlg,
You state "no headspace problems". Have you actually checked the headspace, then checked THAT against actual rim thickness? Factory brass is notoriously often under "spec". I'll bet the actual rim thickness is thin enough to give you those backed out primers. The case is holding tight enough not to stretch, and is giving the primers room to back out.
You might try lubing (lightly) one case, and firing it to see if something different happens. I'm guessing you will see a flattened looking primer - caused by the primer backing out, then being reseated when the case slides back to the breech face.
It looks like high pressure, but it isn't.
If that's what happens, then lube cases to fireform, then back off the sizer so the shoulder is just kissed. Shouldn't happen anymore. Hope this helps,,,,,,,,,,Bug.

Bug, I believe you hit that one on the head!

The headspace was checked,it will completely close on a go gage and will not close on a no-go.The case rims actually measure a couple thou. thinner than the go gage.I'm sure you guys are very right.Should an actual cartridge case be used to ream to correct depth or will this result in other brands of brass not chambering? Thanks Much!

I have found that Jamison's brass has a tad thicker rim than Hornady's, around .006" IIRC.