I've been sleeping for 1 hour. At this point I qualify to take the benefits of a short rest
even though I was hoping to take a long rest.
I can choose, at this point, to either:-
* take the benefits of a short rest
OR
* not!
The 1 hour's sleep I have
already just had was not 'short-rest sleep' or 'long-rest sleep', it was just 'sleep'.
I think that even you would rule that 'sleep' is not more strenuous than 'eating/drinking/etc.'
Okay, at this point (1 hour into sleep) I get awoken by cries of, "Orcs! To arms! We're being attacked!" and the DM asking the players to roll initiative and skill checks to determine if we are surprised.
That is not 'strenuous activity'! Not for me, anyway.
Other people fighting does not prevent me 'not doing anything stressful', and so nothing prevents me from taking the benefits of a short rest at this point.
Of course, as soon as I leap up and start to exert myself I cannot gain the benefits of a short rest
while I am in the middle of exerting myself, but I can certainly say that I've just had the benefits of a short rest
before I actually join the combat that is raging around me!
I'll take it even further. Same set up (1 hour's sleep) but what wakes me up is a hammer to the face, damaging me! Can I then claim the benefits of a short rest, such that the hammer damage comes off my hit point total
after several of my hit dice are rolled to regain hit points as part of the benefits of a short rest?
Yes! You might say that the hammer hit my face before I declared that I was taking the benefits of a short rest, but the reality is that my short rest
was already completed before the hammer fell, because the hammer hit me
after my 1 hour's sleep.
You might suggest that the game doesn't work that way! The game doesn't allow you to
retroactively declare things, does it?
Oh yes it does! A couple of examples are
shield and 'knocking a creature out'.
For the spell, you cast it as a reaction to 'being hit', and the spell may result in you
not being hit. Does this result in a time paradox where now that you were never hit so that you cannot have cast the spell which means you were hit which means you can cast the spell but now you were not hit....forever,
ad nauseum? Does the javelin actually go through your skull, killing you, and
then you cast
shield so that the javelin slides out of your head? No. What happened is that if the javelin
would hit you, you cast the spell which interposes a magical shield of force which prevents the javelin ever hitting you.
So the game mechanic retroactively lets you change what happened
at the table, but nothing retroactive happens
in the game world! In the game, you threw up the
shield just in time!
The game mechanics for 'knocking a creature out' (PHB p198) say that when an attacker drops a creature to 0 hit points with a melee attack (which, according to the rules, kills it) the attacker can knock the creature out
instead of killing them. You have to make the choice at the time; you can't kill him and then decide he's alive again a couple of rounds later!
So what actually happens here?
At the table, the player hit the orc with his axe, doing 12 damage. The DM says that this kills the orc. The player says that he's going to knock the orc out cold with the flat of his axe. This is how the 5e rules work.
But what happened
in the game world? Did I kill the orc, then bring it to life again? No! What was retroactive
at the table was
not retroactive
in the game world! In the game, my blow was with the flat of my axe
the whole time.
It's the same with taking the benefits of either type of rest.
At the table, the DM might announce 12 points of hammer damage to the face
before the player announces that his PC took the benefits of the short rest
he has already had, but
in the game world the 1 hour rest (and the benefits thereof) came before the hammer to the face.
That's how 5e works.