> I don't think even half of it turned out to be factually correct in the end, meaning less truthful than randomness.

This implies a 50% chance that a randomly generated statement is true, which--without getting into the weeds on the generative model--is certainly false.

For example, I can generate random statements of the form "I am X years old" for X \in {1, ..., 100}.

Far from a 50% chance that the statement is factually correct.

> without getting into the weeds on the generative model

No, that very much depends on the weeds of the generative model. I can generate random statements of the form "I am not X years old" for X \in {1, ..., 100}.

Also far from a 50% chance that the statement is correct.

If you limit to true/false statements, it is 0.5

"Water, water, everywhere, so let's all have a drink"

-Homer Simpson

why don't you try it out and report back?