A character can be in a faction and having as many ships there as it wishes as long it's faction tagged, and the very same character can fly as untagged Freelancer with an FL-ID. The same character cannot be in two different factions though.
Could you link not only the quote but also the link from what thread that quote came from? I believe that's a different context you're trying to give me here. Wouldn't be the first time, after the thing with the sanction.