I can definitely see why one might read my comment as presenting a dichotomy, which is why I was actually very careful to not do that in my formulation.
Well, except that I am talking about true randomness (which I doubt exists, but we haven’t proven that on the quantum level). The more colloquial definitions of randomness, I count towards badly understood inputs or just a lack of inputs.

Thing is, if we add true randomness to an input-based decision, it stops being predetermined, but there’s still a logically conclusive choice you’re going to make, based on the incomplete inputs you have. You cannot ‘freely’ decide to not pick that choice, because you have literally no reason not to pick it.

Even if you think, you’re going to pick the ‘illogical’ choice for a change, that is still part of your inputs. It’s likely even baked into our genes, because what appears logical is often not actually the best choice and those who successfully experimented, ultimately survived+procreated.