Legend:

S -> statements
P -> propositions
N -> non-propositional statements
T -> true propositions
F -> false propositions

I don't agree with condition S = ~T + T.

Because ~T + T is what you would call the set of (true and false) propositions, and I have readily accepted the existence of statements which are neither true nor false. That's N. So you get S = ~T + T + N = T + F + N = P + N

We can just taboo proposition and statement as proposed by komponisto. If you agree with the way he phrased it in terms of hypothesis then we're also in agreement (by transitivity of agreement :)

(This may be redundant, but if your point is that the set of non-true statements is larger than the set of false propositions, then yes, of course, I agree with that. I still don't think the distinction between statement and proposition is that relevant to the underlying point because the odds ratio is not affected by the inclusion or exclusion of non-propositional statements)