This may or may not be more information than you want to know. I'll try to explain SAAMI drawings as I understand them regarding headspace dimensions.
On every SAAMI chamber drawing there is a headspace dimension listed identified by an X with a circle around in. It lists a minimum and maximum value. This is ONLY on chamber drawings. The headspace measurement is taken from the chamber end where the case head would sit to a spot on the shoulder angle called a datum point. It is also identified by an x with a circle around it. If you can visualize a perfect circle sitting on the shoulder angle that is perfectly squared and concentric to the overall chamber centerline that's how it is specified to land. The specific diameter of that circle for the datum point is also specified on the chamber drawing. There is no minimum or maximum for that diameter. It's always the same. So the distance between where the cartridge base would sit to that datum circle constitutes the headspace measurement.
There is no headspace measurement specified on a SAAMI cartridge drawing which is what is posted in the thread above. There is the same datum circle identified as was identified in the chamber drawing to the base of the case. That number is listed as a maximum length with a tolerance number by which the case can be shorter. I do not have a 30-06 set of chamber and case drawings sitting in front of me at the moment so unfortunately I can't tell you right now what those numbers are. If you'd like to know I can print a drawing later when I have access to a printer and let you know.
So, that's all well and good. But here's the thing about comparators that can cause your eye to twitch uncontrollably if you don't understand them. A comparator such as the Hornady version has multiple inserts for measuring various cases. The user selects the appropriate insert for the case being measured. It is highly unlikely that the insert is going to contact the case shoulder at the exact spot that the datum line/circle would. The inside diameter of the insert is not going to match the datum diameter exactly. So you aren't going to get a perfect measurement.
So what good is a comparator? It will still provide us a reference number. In your instance, I would take a case fired in your son's rifle and measure in with the comparator. That fired case will come very close to matching the chamber. Some will argue it can take multiple firings and neck sizing only to get really close and that's true but we'll still be within .003" or so 90% of the time. Next, take a piece of the brass you pulled a bullet from and haven't resized and check it with the comparator again. It will be several thousands longer in this particular instance. That additional length is why that case won't chamber in your son's rifle. It's not going to be *exactly* the difference, but within .003" and perhaps less.
Edit to add - I think a lot of the confusion surrounding headspace measurements have to do with the fact that it is based off the datum line on the shoulder and NOT from the base of the case.
Sorry for the long explanation and hopefully it's not too confusing. It makes sense to me when I read it but if something isn't clear feel free to ask.