I had a whole post written up about why I think they definitely would have needed to use the KH team to make higher res versions of the DS assets (or at least, who better than the KH team to recreate KH assets?), but there's too many variables I don't know for sure so I decided not to post it. But basically, if you were to render a PS2 game in HD it wouldn't look that different than the ports in the HD collections at all. DS games, not so much.
The thing I'm not sure of is whether higher res versions of the DS assets already existed. You'd think they wouldn't (all renders of the Days exclusive bosses are definitely their DS models), but higher res versions of the BBS assets seem to have definitely existed ahead of time. The PSP is higher res than the DS, so perhaps this makes sense... but assuming they didn't exist, yeah, they would have to recreate them from scratch, and like I said, the KH team would definitely be the best suited to making models in the KH art style.