I think there's a sliding scale at play - to have agency, players must have the information to make meaningful decisions. The better the information they have, the more meaningful those choices, and the more agency they have.
That being the case, the use of random tables does indeed reduce their agency, at least somewhat.
That said, while it's definitely a good thing for players to have agency, I'm far from convinced that they should have total agency. It's valid to expect them to have to make some decisions based on imperfect, or even no, information.
(Incidentally, the example in the OP also provides a false dichotomy - do they take the quick and dangerous road, or the slow and safer one? But they have other options - stay where they are, find a different way to travel, or perform research to determine how and why one route is more dangerous than the other. That last option shouldn't be overlooked, and if done successfully should indicate that the dangers appear to be similar in type but double as frequent on the more dangerous route.)