You're mixing up terms a bit...
COAL - cartridge over-all length - is from the base of the case head, to the tip of the bullet
Headspace is from the base of the case head to a specified datum line on the case shoulder (specifically 1.630" to the midpoint of the shoulder where it measures 0.400" in diameter, on a .308 Win).
The factory reloading manual shows a COAL or OAL of 2.800" because that should work in pretty much any gun chambered in that caliber. The data provided by the previous owner is specific to your particular gun, optimized for that barrel. COAL is more common when you want to say, make sure the ammo will feed out of the magazine i.e. the OAL has to be shorter than the inside dimension of your magazine. Remington 700s (used to) have shorter mags, so you see 2.800" a lot for short action cartridges. Savage magazine boxes tend to be longer, so you sometimes see people running ammo seated longer, to where it may be closer to the throat of the chamber... in which case you need to use 'Base To Ogive' aka 'BTO', which you get by using a comparator that fits over the ogive of the bullet. Unfortunately these give you a 'relative' reading - one comparator may sit on the bullet ogive differently than another, particularly if they are different make/model.
Unless that guy gave you the comparator he used to get determine that setting, the 2.847" COAL is 'ball park' at best. There can be up to 20 thou variance in the tips of many HPBT bullets, so just measuring off COAL is a little sketchy, and will get you into trouble sooner or later.