It's a matter of scale. At the highest level, of the individual, if you present them with two options, they will chose one of the options. At that level, the question is a trivial: yes, obviously they have "the capacity [] to choose between different possible courses of action unimpeded."[1] Your description was just an explanation of how they choose. If you then ask if the individuals also have "the capacity to do otherwise"[2] then that depends on whether things are deterministic or probabilistic. If they're probabilistic, then yes, otherwise no.
In all three cases, yours and my two, the question is answered trivially and uninteresting. The real question philosophers are asking, I'm told, is whether people have moral responsibility or not. It's interesting psychologically too, should you really feel guilty if you couldn't have done differently?