Bad reasoning, sorry. Infact saying it in public may be a form of riya depending on your intention e.g. if you're doing it so people think that you are someone who does istighfar and thus give you some respect or acknowledgment, then that may be a form of riya, which actually adds on to your sin rather than disipates it :S. That is why, if I am not mistaken, it is reported in hadith that Prophet Muhammad PBUH said that he feared this thing more upon the ummah than the dajal (CORRECT ME IF I'M WRONG)