Delta tried this when CO was planning to not use their EWR-RIO rights (and make GIG service an extension of SAO bound flights). This forced CO into providing n/s service from EWR to RIO.
I'm not sure that the DOT will really find DL's argument appealing. Three US Flag carriers currently provide service from NYC to SAO, plus RG, VP, and now JL. If DL were petitioning for rights from LAX, which has no US Flag service to SAO, the story might be more appealing.