To quote the Adam Ant song:
"Bang bang, you're dead,
Did not, did too..."
As a kid, I played soldiers, cops and robbers, cowboys and Indians, and all kinds of other games with my friends. It always ended as soon as the "shooting" started, because everyone always insisted that they'd hit, but no-one ever wanted to be shot.
For me, RPGs have rules to prevent this kind of thing and offer an objective standard for sorting out these conflicts.
This is, definitely, very true. However, its illustrative to look at, let us say, a comparison of a scenario using B/X D&D (or similar, I don't want to get hung up on specific rules) and Dungeon World (again hoping not to get hung up on rules debates). Let us say that a goblin is holding my character's prized hireling at knife point! For D&D this is a combat situation, primarily. Now, my character can try invoking the Parley rules, those are handy, there's some reaction tables, etc. Maybe the result is good, maybe not, roll to find out! Otherwise we're stuck with initiative, rolls to hit, damage, etc. which is not the most flexible. The outcome could easily hinge on things like whether the goblin does a certain amount of damage, etc.
In Dungeon World I have the ability to state what my intent is, so we can get more or less granular. This could be interesting! Now, note that the focus here is on mechanics serving story more than resolving situation. That is I might make a move to disarm the goblin by hitting him with a rock, or I might make a choice between Defend (I fling myself on the goblin, taking any blow he tries to land myself) and Hack & Slash (I try to slay the goblin by attacking him before he can kill my hireling). Note that "kill the hireling" isn't really regulated by any quantified mechanics in this system, it is merely a consequence of my own actions and perhaps the pass/fail/mixed result action resolution rule of DW (as modified by any specific move). In other words, it would be understood, probably spelled out by the GM, that the consequences of a failed Hack & Slash would be 'dead hireling'.
I mentioned 'granularity' there WRT Dungeon World. This is an interesting trait that non-quantified approaches have, which is, you could focus very tightly. The GM and myself could detail the action resolutions right down to the level of how and when I grab hold of the hilt of the goblin's dagger as I rush him, the counter move he makes to get it free, whether I shove the hireling away in that instant, or wrestle for the blade, etc. DW will easily handle action at this level or any other level (like just adjudicate the entire thing with a single toss of dice, or even no dice at all).
So, there are equally rules in both systems. In some respects they aren't radically different. But they do serve two subtly different purposes. The B/X rules are as you say, "how do I adjudicate 'bang bang you're dead'?" The use of dice here is intended to relieve the GM of any pressure to decide things a certain way, or accusations of bias, etc. Mostly it lets him give bad news without needing to take full responsibility for it! DW's system is more 'facilitator of drama', it doesn't actually talk much about the details of quantified results, nor rest on a certain menu of options.
Finally we could talk about how 'Free Play' comes in here. Certainly in B/X (and nothing stops this from being true in DW either, though it is less needed) the GM can put on his referee 'rules master' hat and start making up procedure to use! There's no theoretical bound to this, it could be used to do things similar to what DW does, or to, for instance declare that a helpless hireling is automatically killed in a single dagger blow, etc. This is fine, though it begs us to ask the question "how is this different from 'bang bang you're dead'?" Well, obviously the GM can ask for dice, so he's got that as an out. However he does have the out of simply having a culturally accepted role AS GM, which is generally reinforced by some sort of rules text. I don't recall what B/X D&D says exactly on this score, but it certainly gives the GM some degree of unilateral 'ruling' authority. DW is more negotiated, so we can say that in that game the GM's saying what happens if X could be more of a consensus thing, but generally if the GM says "that's move X" it usually stands.
So ONE thing we can conclude is that rules are inherently advisory, that GM authority varies but at least as much in terms of 'cultural acceptance' as anything else, and that the default processes (system) of different games will, at least, resolve things on a basis of different agendas, and could do so at different scales, with some games hard coding their default granularity, and others being more agnostic (though I think it is fair to say that DW has a TYPICAL granularity, other games may not).