Well,Bob,i don't want to speak for Square_peg here,but i think what this thread is about is the relocation of some of the "reserve"(put it that way) mass from in front of the eye to further towards the edge,as Necessary.
So(thanks for that,Hacked)the guy with that Connie only wanted to relocate enough metal to restore the shape of the toe,and it appears he accomplished it just as planned.
And to do so it looks like he didn't need to get too close to the center-line of blade,but found enough to move closer by the edge(and then ground it to come up with that "bevelled all around" grind,not sure what the technical term would be).
(the gent is obviously a farrier,i really like the use of that little gas clam-forge,seems like a perfect tool for heating an axe

.
The phantom bevels per se are a radical version of the principle involved,it's probably maxed out in that form,or nearly so.Where nearly all the available mass is moved towards the edge to begin with.
There's also an old method that haven't been mentioned here-modeling the proposed forging process in playdough,or better Plasticine(any non-hardening clay type of substance).
It's never the Whole story,forging is more complex than that,but it does work well for a bit of a preview of the potential,planned solution.
So say you have a worn axe that you're considering repairing in this wise,you could model it in plasticine,and determine fairly exactly where the needed mass is to come from,and in which way it'd be best to move it to where you'd rather it be.