That looks like a test of my personal ability to form correct first-impression estimates.

Precisely.

Also "will prove to be sound upon further inquiry" is an iffy part. In practice what usually happens is that statement X turns out to be technically true only under conditions A, B, and C, however in practice there is the effect Y which counterbalances X and the implementation of X is impractical for a variety of reasons, anyway. So, um, was statement X "sound"? X-/

Ah, I see. "Sound" is not the right word for what I mean; what I would expect to occur if the thesis is correct is that statements will prove to be apposite or relevant or useful - that is to say, valuable contributions in the context within which they were uttered. In the case of X, this would hold if the person proposing X believed that those conditions applied in the case described.

A concrete example would be someone who said, "you can divide by zero here" in reaction to someone being confused by a definition of the derivative of a function in terms of the limit of a ratio.