I wouldn't say "that's all." If it actually does admit nondeterministic solutions (I am not convinced that there is no property or axiom buried in the formalism that forbids this case somehow), then the next question is, does quantum mechanics, which implies classical mechanics, admit nondeterministic solutions? If not (wave mechanics has a way of ignoring weird stuff when it only happens at a point), that would make quantum mechanics a consequence of determinism, a fairly shocking possibility.