Historical example

Suppose a study says:

“Real wages increased by 20%.”

That may be completely true.

But the study doesn't examine:

working hours;

housing;

mortality;

workplace injuries;

child labor.

Then the conclusion:

“Workers therefore experienced a substantial improvement in overall well-being”

may be misleading.

The original fact can be true while the broader inference is inadequately supported.

Therefore:

False is the claim itself is wrong.

Misleading is the information may be true, but its selection, omission, framing or presentation causes an inaccurate overall impression.

This distinction is particularly important for your broader argument about institutions.

An institutional system does not need to manufacture false facts in order to produce a one-sided or incomplete picture.

It can influence:

which true facts are investigated, published, emphasized, taught and remembered.

And that is precisely why the argument about gatekeeping should be formulated carefully: selection can shape the epistemic picture without necessarily making every selected proposition false.