This is a really strange anectode to me. I have never heard of anything like this in D&D. In this example, does the Player have any agency to declare what WILL happen, and the DM always complied regardless of the result? Or is it just the Player declaring that the character is attempting to do so-and-so?
My D&D experience goes like so:
Player: "I cut his head off!"
(rolls to-hit: hits; rolls damage: 5 damage)
DM: "The orc shifts away, and although you fail to cut his head off, your axe does nick his shoulder. He takes 5 damage."
(If, however, the damage brought the orc to zero hp, then heads go rolling.)