"Rigging" could only really be in the judge votes. I doubt they'd get away with miscounting public votes.
I think people at home saw through Mario's insincerity somewhat. Emmitt is nothing if not sincere.
Plus, if Mario had only admitted to his obvious relationship with Karina, maybe viewers might have actually been somewhat charmed by it. That is, supposing they weren't familiar with his previous somewhat sordid romantic history.