Not to be contrary, but it sounds like you are contradicting yourself.
Well, my opinions apply to actual play in the "real" world, so the situation is practical, rather than absolute, but I don't think there is any basic contradiction, no.
The GM setting scenarios and background in advance, according to a set of guidelines and design objectives, is one thing - the GM judging the worthiness of a player's approach during actual play is another. In theory, the scenario design can happen during play - often known as "winging it" - and be quite acceptable within my proposed approach, but it is very easy to slip into "judgement" mode while doing this, deliberately making the challenge to the character easier or harder depending on your opinion of his or her ideas. This is definitely an example of "GM skill", but not one I see often explicitly stated.
In your view, when is the system making assessments of outcomes and when is the real person DMing making these judgements?
When the chance of success for a given situation is explicitly given by the system, then the system is making the assessment. This applies whether the assessment is based on the setting/game world design ("it's a rocky wall with handholds, so it's DC 15") or on metagame concerns ("this is a 7th level Moderate challenge, so the DC is 22"). If the GM makes up a DC based purely on what a player says their character will (attempt to) do, then the GM is making the judgement, not on the game or world situation, but on the feasibility/good sense/coolness of the idea the player has proposed.
Obviously, there is a "grey area", here. If the player decides that their character will try something not envisaged by either the system nor the GM's design of the "encounter space", then a defined difficulty may not be available. Where absence of player input to the outcome is important (generally, where there is some competitive "game" element among the players), a system can handle this via "catch all" default difficulties and player resources (such as "action points") to keep the outcome "system decided". Where player input is not an issue, the difficulty can simply be set by agreement, vote or whatever among the players (such as the system in Primetime Adventures). I find either of these options better than the GM being judge, jury and executioner all rolled into one.
Also, how do players explore a setting, situation, or character when they are the creators of these?
Have you never sat and reflected on some situation, exploring the ramifications of it? Players who have experienced "immersive character play" often talk of "suddenly realising that the character would do X"; they have just discovered something about that character. Exploring our own imaginations - either alone or with friends - is a pastime with a long and storied (literally!) history.
Try Universalis for a game that makes such collective exploration explicit in its systems.
This stands in opposition to a DM where these things exist outside of the players.
If the entire thing is exclusively in the GM's imagination and no one else's, I don't think it's even roleplaying! The situation, setting and action must, at a minimum, be communicated to the players so that they may "see" it in their imaginations. Even then, we have only reached the baseline of "storytelling"; to make it "roleplaying" the players must have
some input into the resolution of the imaginary situation. Thus, I don't see any roleplaying circumstance where the imagined action exists wholly "outside of the players" - what we are discussing is thus not "whether or not" but simply a question of degree.
The latter here sounds like playing "Guess what I'm thinking?" with one's self.
If by "oneself" you mean a gestalt of all the players present (including the GM), then yes, maybe that is so.
