I'm mostly familiar with macro and finance applications; I'll take your word for it that it's not strictly coming from agent rationality in other subfields. Perhaps I should have said, "unforcastability" which would have covered natural experiments and IV as well.

Oops. I wasn't thinking about macro when I disagreed with your earlier claim. Your explanation sounds consistent with my distant recollection of the field (though I'd also take your word for it.)

I shouldn't have disagreed so strongly in the first place.

Maybe the fact that moment conditions are often first order conditions for some agent's optimization problem is why rationality was mentioned, but I'm just speculating.

That may have been why it was mentioned, but within micro applications, that is getting the relationship flipped.

Micro models estimated from agent's optimization problems are more frequently estimated using MLE (John Rust's GMC bus paper being a canonical example, though still true in the current literature e.g. Nevo, or Bajari and Hong).

Micro models estimated from aggregated data frequently lack agent-level optimization, and those are the models more frequently estimated with gmm (examples here would include the hundreds of papers based on Berry, Levinsohn and Pakes).

So, this explanation doesn't seem to hold in micro contexts.

Though, as the previous commenter pointed out, macro is quite a bit different, and your explanation is probably correct there.