The return particple "se" is not needed here? I translated it as: They knew about themselves, but that was wrong.
"se" does not belong here at all. But actually, your translation might be acceptable.
But I remember other questions with "each other" with "se" participle. But yes, with "věděli" this participle seems weird to me. May be there were other verbs.
Not saying the other exercise was exactly this, but Znali se. is a good example with "se". One of the differences between the two verbs is that "znát" takes the object in accusative, while "vědět" cannot use a preposition-less accusative object if the object is a living being. Vím to. is fine because the object is a generic inanimate "it" (being inanimate is not really a sufficient condition for the sentence to work, but it will do for now), but Vím tě. is just wrong. The verb "vědět" can be associated with the more loosely connected prepositional phrase of the "o kom/čem" type, where the part after the "o" must be in locative, and that for the reflexive pronoun means precisely sobě.