Again, I think even if just comes down to you making a 50/50 call, the choice is meaningful because the consequences were death. I agree it isn't an informed choice. But it is a very real choice and it wasn't a meaningless choice in way it would have been had, were this an RPG, the GM simply said 1 in 2 chance, which ever direction you choose a car T bones you, because in that instance which direction you choose doesn't matter at all, in the former instance which direction you choose very much mattered (it wasn't a puzzle to crack, your choice may come down to a whim on your part, but it mattered). And that is a very far end of the extreme of the choice not being informed.
I just literally don't grasp how this is logical in any way whatsoever. Sorry. There's absolutely no difference between me saying "Gosh, I have no idea I'll randomly choose to go left" vs "I flip a coin, heads is left." I mean, I don't say this to argue with you, it is simply not sensible to me, I can't grasp how they differ in any way.
Most choices will fall on a spectrum (another example you may have some indication things are a miss: i.e. you hear on the radio a bank got robbed three blocks from Wyoma Square to something even more informed like you see series of bad omens the closer you get to the bus). But I think even when the choice is essentially made in a vacuum there is a large difference between one where your choice is going to result in disaster or a normal day; and one where your choice has no input into that. The former I would label a meaningful choice.
I mean, sure what action you took has CONSEQUENCES, but I dispute characterization of it as a 'choice'. No choosing was involved in a case where there was nothing to go on. To call random stochastic firing of neurons as choice reduces the term to meaninglessness IMHO.
Now, I agree, there's a whole range of how informed someone is. A rumor, a faint bad smell, a map that says "do not go this way!" (but may be a trick), and so on and so forth. Nor would I expect choices to generally be perfectly transparent either, certainly they never are in the real world. However, if we have this no-information situation certainly the 'choice' cannot do any work in terms of informing the quality of our role play, right? I mean, I am not learning anything meaningful about my character, or establishing anything meaningful about her, if I simply say "meh, I always go left..." Sure, its a fact, but we can't conclude anything much from it.
The point, ultimately, being we need some sort of informed decision making. I think, personally, informed agenda setting is even better. You can get a version of that in, say, a sandbox, we go to the castle or the temple, and we have reasons for choosing one or the other. The most powerful version, in a character development sense, would be "I think there's a temple of my patron god Rumple over to the east, and I have heard they need help!" That can be a fun way to pull in what the players are looking to do, and is part of what I think something like Dungeon World is about.