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".
You are very dismissive of other people when their argument clearly leaves your own without a valid leg to stand on, something I find highly irritating.
If you tried to pull nonsense like that at my table in an attempt to abuse the rules you would find that it would back fire in your face on a regular basis.
Player: Ok, after we are done resting we leave the dungeon to talk to Jimmy ... the ... umm ... the Keeper of Library ... to ... uh ... to ask him about the stones ... in ... the dungeon. Then we rest again. Then we go to the market to have err... Tim the swordsmith take a look at the knives we took off the goblins. Then we rest again. Oh and during each rest my fighter will use second wind.
DM (option 1): Ok, as you enter the library you find that Jimmy is not actually there, which is strange because, as you know the old fellow practically lives in that Library. The library seems oddly silent... even for a library. When you look around for the section of books dedicated to stones you round a corner and bump straight into a gaunt looking man wearing dark robes, who is staring straight into space. He doesn't seem to react to your presence. What do you do?
Translation: Turn the banal attempt at extracting more undeserved short rests into new and interesting (possibly dangerous) events that sends the adventure in new and unexpected directions.
DM (option 2): Ok, upon your return to the dungeon many hours after you have left to talk shop with Tim and get Jimmy's expert opinion on the stones used to construct it, something seems to have changed at the etrance of the cave. Where it was clear before long sharp sticks with jagged thorns dripping with some dark substance now criss cross the entrance, jammed into the ground and the side walls, bound together with rope to form a rather nasty looking barricade. You have no idea what lies in the darkness beyond ... but you doubt that this barricade got here by itself.
Translation: When you leave a part of the world to try and get more undeserved short rests the world doesn't stop and simply wait for you to get back. Pressing on and clearing a dungeon (for example) has an advantage: the dangers within do not have time to properly organise themselves against you. If you leave for 5 hours ... then they do and they will. So when you return things are much harder and more dangerous than before because now they are ready for you.
DM (Option 3): Err... no you don't. In that time you talk to both Jimmy and Tim. They give you the information that you need. When you are ready to return to the dungeon your short rest ends and your abilities that require a short rest are available once again. If you left the dungeoun to try and get more rests and free healing, next time don't bother. That is not going to work. Do you have and issue with that?
Player (option 1): Yes ... blah blah blah...
DM: Then you can leave.
Player (option 2): No that's fine.
DM: Great, then let's continue.
Translation: DM rules rule. Fullstop.
Oh and reading the rules and applying them is not rules lawyer-y. Don't be so dismissive and rude.
Going all hyperbolic over rules-issues and supposed flaws in a game not yet released from readings of a character sheet ... I wonder what we could define someone as who did that?
Oh wait ... let's not, that might be rude.