Javi Martinez isn't a CB either, he's a DM being played at CB and he's stated he'd rather play in midfield.
Barca could always go for Dede from Vasco, he's been bigged up alot lately.
You're nitpicking, he's shown he's extremely competent in both positions and could easily spend the rest of his career playing CB to a high standard, especially at a team like Barcelona who spend very little time in their own final third. Unlike Song. Who's also not good enough as a DM either.
Song did weirdly get a lot of assists last season, but I think that was mostly due to VP's ability to turn anything into gold. So in that respect I'd say Song can spot a good pass and play the occasional killer ball, but his midfield passing can be sloppy. And given how much midfield elaboration Barca like, I can't see him fitting in well.