I think one could also apply the "from a certain POV" thing too...
In the prequals we see that there are force adepts that the Jedi simply abandon due to age or whatever reason. So they're out there, floating around... I think it's entirely possible that, while in his travels and general rompings in the galaxy, Anakin befriends a force-adept that the Jedi aren't willing to train for whatever reason... But Anakin maintains a "friendship" with him. Call it an apprenticeship if you want, but I could also see a simple friendship being construed as that as well... they talk, maybe Anakin shows a trick or two to the guy... As he gets older, he maybe developes some of it himself too... When Ani becomes Vader, he then says, "hey Joe... Wanna see something REALLY cool you can do with the force?", and now he's really become an apprentice and such...
Anakin's possible befriending and unintentional mentoring an abandoned force-adept is something I can bite on... I think then the title of "apprentice" is really just from that "certain point of view" and nothing more. That, at least to me, can squeeze this into believable EU in my world anyway, if that makes any sense at all Jason.
But him training (intentionally) a force-adept in secret in the ways of the darkside and things, long before Anakin is actually evil, well that is nothing I'd bite on I don't think.