I agree with most of that, GunPlummer, but no one is talking about "jumping the string".
Jumping the string is virtually impossible with modern archery equipment unless the deer is LOOKING at the shooter. The bows are so fast that the animal as no time to react to sound inside about 25 yards and so quiet that the animal will not hear or will not react beyond about 25 yards.
The point, though, is Time of Flight. It takes a modern bow about 0.6 seconds to send an arrow 50 yards. That's about how long it takes a rifle bullet to go 500 yards. 25 or 30 years ago, that 0.60 seconds would only get an arrow 25 yards. Even today, there are guys hunting with recurves and long bow that take that long to get an arrow 20 yards.
If the ToF is the same and the objection is that the animal has too much time to move, then a 25 yard shot with an old bow is just as unethical as a 500 yard shot with a rifle or a 50 yard shot with a modern bow.
Interestingly enough, I see no one able to quantify just exactly what is "acceptable risk". Since the original story in the OP is a claim that a deer was able to move too much even at 100 yards, why to we say 500 or 400 or 300? Is not 100 too far? If not, why not? What IS the acceptable risk? What range? More specifically, what ToF, because that crosses all the barriers between cartridges and weapons.