It was a choice using offensive options though ones mechanically endowed by the game even if it was less offensive than the other. It did not occur at the point where you were already being attacked but in a rare window (but yes concentration is nice) how do you react to that sweeping sword blow or already launched fireball remains passive and not a tactical choice regardless if you hand the player the dice or roll yourself. And really who rolls the die is the functional context we were talking about .... i am saying I would like more than just that. For instance if the choice allows my character to move gaining a defense bonus but penalizes subsequent attacks that would be an example. (that reactive move might advance my goals of escaping regardless of whether I still got hit)
Ulterior motive - The tactical choices in D&D land are generally way too dominated by FOCUS FIRE....this could reduce that benefit a bit - Note if the character does move and lose some to hit the choice to attack more enemies instead of focusing may improve your defense when you are surrounded. (even if the attacks became at a penalty)
Actually, the 1hp was a result of hellish rebuke, explicitly a reaction to an attack hitting, and the save reduced it to 1d10 and they rolled a 1.
It was "endowed" by the player having made the choices that gave that PC that option.
I honestly see no connection between who rolls the die and what choices are made.
But, while I dont share maybe your keen division between an offense and a defense, there are a good number of similar options characters can have built into their characters
if this kind of reactive defense is desired.
Shield spells come to mind and are easily available - magic initiate feat or class level.
Absorb elements.
Battle master has some reactive defense maneuvers- also martial adept open those up to plenty and I have reskinned them as "magic tricks" to explain that fest for an illusionist.
Mobility may make spreading attacks across a couple folks to prevent them getting AO as you trot by.
Rogues have "use reactions to..." kinds of defenses
Depending on bard schools - inspiration die can serve a lot of purposes, I think even one might be able to hit enemy concentration checks. Have to go look.
Isnt there a "you swing st me I make you hit thrm" - maybe under a monk?
Heck, I even had a character "ready the dodge action until blah blah " so he wasnt dodging when the minion struck him and waited for the heavy hitter to go after him only realizing he was swinging at a dodger instead of other easier tu hurt targets.
Basically, not gonna try to cover all the various ways but, if you want reactive defensive choices, there are a lot of them and you can create a character who has those at their disposal.
But I dont know what thus has to do with what die who is rolling or zing.., so...
From a narrative standpoint, when the PC makes his armor roll vs the orc swing I narrate using the same tools I will when I roll for the orc, like ssy in a pick-up game. Seems to work fine.