The reasoning does seem to have some obvious issues, but rather than trying to correct them, I think it's worth thinking of what it is at root trying to say in terms of the philosophical school of Logical Positivism.
Very much out of fashion in analytical philosophy as a methodology for conceptual analysis, the basic idea of Logical Positivism/Empiricism is that the meaning of a statement should be strictly given in terms of logical conditions under which the statement would be verified or falsified. If there are some statements under which there are no strictly logical conditions under which they would be verified or falsified, those statements are treated as strictly nonsensical. And since we cannot tell nonsensical statements apart (because they have the exact same verification/falsification conditions, i.e. none at all), nonsense is nonsense is nonsense.
So if we take it that the future really is factively undecided, such that there is no way for us to even in principle validate what will happen in the future from our current standpoint, then a logical empiricist might denounce all future case statements as devoid of meaning. And so by a simple meaning-theoretic substitution principle, they can plug any old nonsense statement they like in there.
If we say that this kind of "verification conditionality" is all there is to meaning, and that truth conditions must be strictly explained in terms of finite proof or empirical procedures, then many statements that we would naturally think to have some kind of simple understanding simply fall out as non-cognate. It's widely recognised, however, that this kind of basic form of logical empiricism is not a good fit for the practice of classical mathematics, and hence for the wider part of science as is in fact practised.
Moreover, it is all too easy for questions about verification and proof to be dominated by subjective considerations that we might reasonably pose have no business being imposed upon objective scientific analysis. Logical Empiricists have a tendency to dismiss an awful lot of things as nonsensical simply on the grounds that they do not accept certain premises. It seems a mistake to think that the actual falsity of a premise makes it logically impossible. Following work by Kripke in the 70's, metaphysicists have widely reintroduced the idea of using simple set-theoretic models to ground talk about alternative possibilities than the brutely first-order factive notion of what can be strictly proven from presently observed and reified facts. This is particularly so if we want to be able to talk in terms of an objectively probabilistic methodology in science; we would like to be able to model counterfactual situations in order to establish a kind of state space framework for probability-based scientific models.
Nonetheless, certain projects might be interested in trying to squeeze out the methodology as far as it goes, and I think we see this a lot in certain "New Atheist" philosophy inspired by evolutionary biology. Strictly grounding mathematics in neuropsychology, for instance, seems to be one way to go about it, and it's premature to think they can't get something interesting out of a "finitistic" conception of theoretical resources by going down that road.