Pretty much exactly what I'd expect a rules-lawyer to say!I've rarely heard any rules-lawyer-y argument that didn't involve an appeal to "but it's just what the rules say!" (i.e. "reading-and-understanding").
The idea that such a power can only be used in "combat" seems real sketchy, frankly. Very 4E-esque, some might say, even.
A group can - it's just likely to be violently different from that of another groups, because that's some vague stuff. I mean, you wouldn't even be arguing this if there was a question about it, so let's not pretend that everyone agrees.
This is all very rules-lawyer-y stuff - by your logic, it'd be fine to rest for an hour, go argue with a friendly NPC for a few minutes and try to convince him of something requiring a check, then rest for another hour, and that'd be two short rests, but if you just rested for the same period of time, it'd be one.
Oy vey.
Yes you need better definition on this than that, if you are going to balance around it. It'd be much easier to just balance around an assumption that every hour resting counted as a "short rest".
I'm thinking more and more the best solution will be that Second Wind could simply be reflavored as a boost of adrenaline (I can think of many fencing bouts I've been in where parts of my body that have been hit repeatedly and are sore start working a lot better with a boost of adrenaline, so even for the "all HP damage is physical damage" crowd, it works) that allows Fighters to shrug off wounds dealt in the height of combat, and is thus not usable outside of combat / situations that would purport said adrenaline.