I can't tell you for sure if it's absolutely always but it's definitely most of the times.
Well to take double accusative is something very simple, it means that the verb you have needs two objects(or, of course, two sets of objects. I mean, there could be 5 objects in total), both of which will be in accusative. The examples you wrote are correct. Each verb has different syntactical uses. Some verbs can take as their object only acc. Others can take only dat. Others take both. Others take acc. or infinitive. Others take a whole other sentence as their object etc etc.In this .pdf
you will see a list with some important verbs of the ancient Greek language. I hope you have a dictionary, if not let me know and there's things we can do(I mean online dictionaries). In this list "τινα" or "τι" equals acc. (τίνα = person, τί = thing). "τινί" = dat. and "τινος" = gen. It's the declension of "τις" of course, which means "somebody".
After reading the sentence again, I understand what you mean about the double accusative and how the books might be teaching the men about Homer's friends. "παιδεύω" can indeed take 2 accusatives, but one of them would have to be the thing you educate about, the object of the education. If however you were to translate the sentence with "about", you would either have a preposition like "περί" which often means "about", or some other kind of hint. (Ta biblia epaideue tous en th agora anthrwpous *peri twn Omhrou filwn = The books educated the men in the market about Homer's friends)
Also, teach = διδάσκω. παιδεύω = educate or raise (a child). When παιδεύω has one object, like in our case, you translate it as "educate". When it has 2 objects, you translate "teach". However, in order for παιδεύω to carry 2 objects, one of them must be a thing, and one of them a person (as in I teach somebody something- you can't possibly have "I teach somebody somebody", which is precisely what we have if we try to translate as teach in our case). In our case we have no "thing" as an object, which is the most important hint towards the fact that our verb has only 1 object.**
*notice there's no comma now that we don't have apposition
**when I say 1object or 2objects, I really mean 1 set of objects. For example the verb of this sentence "He taught John, Mary and Lila maths, physics and history" has 6 objects in total, but only 2 sets of objects, one set contains the "somebody"'s and one that contains the "something"'s (as in "I teach somebody something"). So, even if you were to assume that both "tous anthrwpous" and "tous filous" are objects, given that they are both "somebody"'s you now know for sure they really are part of 1 set.