I could not quickly find my HK blueprint, but here is a similar copy posted on this site by another member. The tip of a 3-lug barrel is the index inside of the can. From the tip down to the lugs. It needs to be .590" +/- .0015 other wise the can (especially a long can) will wobble and can cause a baffle or cap strike by the time the bullet gets near the end of the can.
The biggest problem is that the thread protector is machined separately. AND a lot of people can thread and knurl a small piece of tube.
Here is the problem-
There are two types of knurling, (1) distortion & (2) Cut. 99%, and most of what you will see or find, is distortion. It is usually meant for gripping by humans, or just traction for gripping a moving belt or something non-critical. It is usually made by 2 rollers pushing or squishing onto the metal (ie Distorting the metal) after the final cut. You have very little control over the ending diameter.
Cut knurling is more advanced and a "newer" process in where the cross hatched pattern is "cut" into the final metal profile (removing to create a valley) leaving the "peaks" at the O.D. the area was machined to, with out "raising" or "increasing" the O.D.
You could distortion knurl and then grind the final O.D. also, but that's another setup process.
A true "thread protector" is just that. It is a protector of the threads. The only dimension that matters is the inside thread for fitment.
However, on a "dual option" HK 3-lug, it is giving you a "second option" for attaching things to the barrel. The knurling is no longer just grip. Therefore the piece now has TWO critical dimensions- inside & outside. Most people don't know, don't understand, or don't care.
I have experience with buying a "high quality" barrel from a popular HK parts vendor, only to find out after cap strikes on a sub-gun that the "thread protector" supplied was NOT from the "high quality" barrel manufacturer, and was instead just a cheap distortion knurled thread protector from another party that the seller chose to substitute due to cost savings. That other party, that was just cranking out less expensive thread protectors to be competitive because a step was being skipped, they didn't know what they were doing, or they were not told what it was being used for. (buyer beware I guess) I blame the "popular vendor" who saved a nickel on matching two different manufacturers. But that is just my opinion. (the barrel manufacture knew the dimensions and the issues, but was asked to NOT supply his protector !)
On a second note- putting suppressors on 3-lugs is another one of those "American" things. HK did not design the 3-lug for a suppressor, it was designed to hold a bayonet and flash hider and some other light weight thing (or something like that). Similar to putting cup holders in a car. Another "Americanized" design.