An opposite for apocryphal?

Solution 1:

Generally, apocryphal is taken as being antonymous to canonical; there is a canon that is accepted (whether the biblical canon, or a "canon of lore"), and outside of that is the apocrypha which is uncanonical.

This refers solely to how accepted each is, not that either is true or untrue, and indeed even in the figurative use you refer to, such apocrypha can still be true, we just don't have much evidence to prove it. Most such is probably false, because there's a lot of people making up a lot of things (even before social media and meme-generator websites), but some such things are true statements where the supporting evidence is forgotten (the problem is we don't know which they are).

For the meaning you are looking for, where the fact is true but not widely believed, I can't think of a perfect match right now, little-known and widely-disbelieved hit part, but not all of the target. A case could be made for occult, but that word has long been associated only with a particular type of hidden fact, and for that matter with many things that are neither facts, nor particularly well-hidden.

Solution 2:

A few words come to my mind right away:

• Religious context I would use tenet.
• Scientific context I would use hypothesis.
• Everyday usage I would use (conspiracy) theory.

Solution 3:

A postulate is

something taken as self-evident or assumed without proof as a basis for reasoning.