So I was checking out a list of the Secret Titles on Serebii, and apparently it's on-sight and Very Fucking Personal™ between these two.
Edit: apparently it was programmed wrong and it should be Silver you fight Gio with rather than Jasmine, since the "I Hate You" title actually features Silver. It would be so much funnier if she just had this UNFATHOMABLE hatred of Giovanni or if he just detested her personally for some unknown reasons.