Does Athreos work on countered or discarded creatures?
What you were told about Athreos triggering for countered creature spells is incorrect.

The official definition of "dies" in the comprehensive rules is:


  700.4. The term dies means "is put into a graveyard from the battlefield."


Since a countered creature spell is never a creature on the battlefield, it didn't "die".

Similarly, a discarded creature card would not trigger Athreos either.

In fact, note the terminology here: "creatures" only exist on the battlefield; they are "creature spells" when on the stack, and merely "creature cards" or "creature tokens" elsewhere.