I don't think I understand the question. When you ask "are they free to engage in those", are you asking about the scope of permissible action declarations? In which case it will depend on the details of the action in question, and whether the fictional positioning supports them.What if there are other avenues of success that the Players/PCs see? Are they free to engage in those, or do they now have to follow he situation you set up that forces those choices?
I'm also not sure what you mean by "follow the situation you set up that forces those choices." When Xanthos says to Xialath, "Vecna and I are going to conquer Rel Astra in the name of the Great Kingdom. If you join with us, we'll make sure you're awarded a magistracy once Rel Astra is ours," Xialath has to do something in response. The obvious possibilities are to agree to join with them in exchange for the prize (as happened in my game), or to refuse the offer (in which case the PCs presumably find themselves at war - not unheard of in that campaign). There's also scope to try and negotiate for some change in the offer (and maybe Xialath did extract additional concessions - I don't remember all the details anymore).
But Xialath's player doesn't have any authority to just stipulate that Xanthos has not asked that question; or that Vecna is not, in fact, planning an assault on Rel Astra.
Well, here's a summary of the "standard narraivistic model":framing scenes can also limit player agency. Would you agree with that? My understanding of the term is that it’s the GM trying to force a decision by a player, right? To go where the action is. Here’s the situation, what do you do?
One of the players is a gamemaster whose job it is to keep track of the backstory, frame scenes according to dramatic needs (that is, go where the action is) and provoke thematic moments . . . [O]nce the players have established concrete characters, situations and backstory . . . the GM starts framing scenes for the player characters. Each scene is an interesting situation in relation to the premise of the setting or the character . . .
In contrast to the GM, the player's role "is simple advocacy", that is, "they naturally allow the character’s interests to come through based on what they imagine of the character’s nature and background." When presented with a situation, "[t]he player is ready . . . as he knows his character and the character’s needs, so he makes choices on the part of the character."
The example under discussion earlier in this post is a bit more complex than that, because the pressure on Xialath's player is coming not just from the GM component of the framing (Vecna's attack on Rel Astra) but another player's contribution via that player's PC (Xialath can have a magistracy if he goes along with the attack). I think this sort of thing is not that uncommon in RPGing.
But in any event, the player built a character with certain dramatic needs. Now those are being engaged. Where is the limit on agency?