Bedrockgames
I post in the voice of Christopher Walken
Yes. They "probe the setting" by declaring actions - generally low-stakes actions - that prompt the GM to reveal more of the setting. This is not moving beyond the GM's "menu", though.
yes it is because it can actually create new things. Granteed the GM is the one who comes up with what it is exactly, but this definitely has the effect of steering campaigns into direction the GM might not have planned on the menu. Just as an example, the GM might have a city on the map and the players might say "Are there any celestial plume dealers in that town we can work with". And the question might be asked literally or play out as the players go to the town and ask around. But however it happens it forces the GM to answer the question of whether there are plume dealers in town. And if the answer is yes, that might become an avenue for exploration. Again, yes the GM will 'author'* the details of that and have final say, but this is definitely in my view the players 'doing whatever'.
*your word not mine