Again, the issue is one of volition. If you always choose the path of the character, then, yes, you may have an unexpected thought, but the character is still just you directing it. You can ignore that thought, use it now and refine it later, follow it, whatever, but this path is solely because you chose it for the character. You aren't engaged with the character, the character is just an expression of what you're thinking.
Here's an example: My current D&D character has a Flaw that they will abandon those that don't contribute. This is tied to backstory, party due to upbringing by a literal ice devil and also due to the outlander background after he ran away and lived with barbarian tribes in the frozen north -- if you don't pull your weight you're exiled. So, a situation came up in game where another character not only didn't pull weight, but made a choice that actively endangered everyone's lives. This should have been a pivotal moment for my character if I was interested in finding out who this character is -- are they the kind of character that will demand this other be exiled or take action against them or will they suppress this and go along because it's for the greater goal? Here's the choice, and it could be one where I get to learn this about my character. If I, like I do, retain 100% control, then I'm just going to pick one of these and express it through my character. I haven't learned anything about the character in this situation, I've instead decided who the character is and then apply that. I chose the latter, because 5e isn't a game where this kind of conflict actually works. Had I been playing a different game, then I might still have chosen but it would cause problems if I did so because my character would have to be working through this conflict -- perhaps I have a penalty or there's a new distinction that can be triggered. Dogs in the Vineyard works like this, in that I can choose to escalate or bail on a conflict, but I'll likely suffer various forms of fallout due to this that pose changes to my character (Dogs is all about this). Other games might make this kind of choice something that gets directly challenged and I don't necessarily have control over the outcome - my character's flaw may overwhelm them and I now have to deal with the fact that my character absolutely wants to toss the other character down an icy ravine to die from exposure.
The difference here is if I'm just picking the outcome myself and can justify it however I want, then I'm just expressing the character I'm choosing. I haven't learned anything new here, I've just decided something new. And, note, in none of the examples I've list above is a die just picked up and I'm told what my character things. These all come from things I've intentionally staked as conflict points for my character, so I've picked these. It's a big difference in how roleplaying can be approached. Although, I'm not terribly surprised at the resistance to the concept because, quite often, this difference gets viewed as one being somehow lesser than the other rather than different. They do different things.
Also note that I didn't once use "explore" in this response. "Explore" is not at all crucial to the point I'm making.