We'll see what Al Palmer is actually interested in knowing. If it is neck wall runout, I see around 0.0025" TIR as pretty typical. I've had Norma and Lapua that were all 0.001" or less. I've got a fifteen-year-old lot of Winchester .308 brass that averaged about 0.003", with one single case that was 0.008" in wall thickness runout. Since this number typically is reflected in the overall bullet runout and centering failure in the chamber, I don't like to see anything over 0.001" for precision loads and will use outside neck turning if I can't select enough from a lot for my precision loads that came out like that by happy accident.
If he is talking about neck tilt or OD runout on a resized case, as caused typically by expander pull, I've seen long necks on .222 Rem and .30-06 give me numbers as high as 0.002" on my Co-ax press, but that's about it.
If he is talking about assembled cartridge runout, I've seen up to about 0.010" loading by hand. The author of that article found worse. But the better article, if you get a copy, is A.A. Abbatiello's article in the old
NRA Handloading book (p.87). He got samples of 42 lots of .30-06 National Match ammunition and measured runout and had good shots fire them in match rifles and got some hard data to show about 0.004" of tilt off-axis, as measured with the back and tip of the bullet centered and runout taken from wobble at the bullet just in front of the case mouth, would open groups about 1 moa. He also showed that number or half a thousandth more is roughly the limit of the effect. Any more tilt than that was straightened out by the bullet entering the rifling. He showed a center of mass error calculation that predicts the effect and he found that if you find the high side of your rounds and load so the high side is at the same side of the chamber, it cuts the error contribution on the target in half.
Harold Vaughn (the price at the end of that link is rediculous) repeated the experiment with a different bullet in 6 mm out of a super-precision integral machine rest gun firing through 100 yards of sewer pipe to eliminate wind, confirming the theory, but the different bullet shape didn't allow nearly as much tilt to remain in the barrel (longer number of calibers of bearing surface, so the bore straightened out more of the tilt; the old M1 Type bullet in National Match ammunition only has a 0.88 caliber bearing surface). His result was a little less than half the group opening effect that Abbatiello got. But he also did a noteworthy thing to test it that the OP or anyone here could try. He took eight cartridges with the maximum tilt and marked the high point of the runout and then fired, loading each successive round 90° clockwise in the chamber from the previous one. The result was a 4-leaf clover group, with two holes making up each leaf, thus establishing both Abbatiello's observation that where the bullet starts in the chamber controls the direction of the drift caused by the center of mass dislocation off the bore axis, and finding the diameter of the group error they imposed.
Below is a drawing I took off Vaughn's information and how it would look if Abbatiello had done the same thing based on his measurements. You can see it makes quite a difference what bullet you are using (Vaughn's was a stubby ogive flat-base benchrest bullet, while Abbatiello's was a longer ogive bullet with an extremely long boattail).