It doesn't matter, the record of the action details are what matter.
As Terry and Dave have explained they keep records on the actions that go through their Shops, as I mentioned doing myself. In fact, I simply took the idea from Dave after having spoken with him a few times.
To the original question, as I read it, can you do a barrel without ever seeing the receiver?
There is one action maker that I have seen repeatable enough to attempt it: Bighorn
I suspect that American Rifle Mausingfield actions will be capable of it as well; knowing the folks making the actions. In fact this very topic has been something that Ted and I discussed recently.
The vast majority of riddle receivers need to be in my hands the first time for proper documentation and after that I can repeat them from the measurements.
I can also do it on a manual machine that does not have a DRO. It takes longer than a CNC lathe for the threading and profiling but it is still possible without much trouble.
The CNC isn't magic and it doesn't make poorly documented processes work just because they're done on CNC.
A great example if that is in this thread already: Jon Addis took your barrel that was already headspaced to your Acton and tried to screw it into 3 other "identical" receivers and none of them fit properly.
Now, I have done otherwise with several bighorn actions, the two I run regularly as personal guns are so close that they not only share headspace but the barrels time identically from action to action. These are both older bighorns without integrated lugs.
The new actions with integrated lugs are even better across the board.
I have delivered barrels to guys without having seen the action a second time, I have also taken requests to match headspace across several barrels so that the guy can determine which is the tightest shooter and use that for matches with the other barrels as practice barrels.
I have not previously recorded the thread lead-in location to track the engraving location as Terry Cross mentions but I don't doubt it's possible, I just need to add the option into my tracking spreadsheet.