I think players need to have complete freedom of action within the scenario/adventure, but they need to be willing to buy into the premise. Eg, in a Call of Cthulu adventure the Investigstor PCs should be free to pursue any avenue of enquiry they wish, to fight, flee, interrogate etc as they wish, and there should not be a preset sequence of unalterable events. OTOH, the players do need to be willing to act as investigators. I recall running the CoC intro scenario "The Haunted House" for my wife years ago, and after a couple spooky things happened, she identified the source as the basement, and, quite reasonably, flatly refused to go down there. She made it clear her PC wasn't crazy and had no interest in exposing herself to danger. Which kinda floored me... In the end the two gung-ho male NPCs with her went down there and sorted out the BBEG by themselves.
I'm currently running a club D&D 3.5e campaign where the premise is that the PCs are the heroes of Willow Vale, defending the land from evil and undertaking missions at the request of the goodly king. There is no place for evil PCs, PCs who take every opportunity to kill the innocent, or cowardly PCs who refuse to go on the mission (although for the latest one I gave the group as a whole the choice whether to undertake it). OTOH, the missions themselves are traditional setting-based adventures (eg B5 Horror on the Hill), and within the scope of the adventure the PCs have complete freedom of action. They could retreat/fail, which would have negative but not necessarily catastrophic consequences.