Even if one whom is not careful regarding non-Jewish bread [during the year], should be careful (during the ten days.) Rema: And there is to every person to search and inspect in their deeds and return from them in t'shuvah (repentance) during the (Ten) Days of T'shuvah. And a doubtful aveira (sin) needs more repentance from a certain aveira, because one that knows regrets more than one who does not know (which is the case when one is unsure). And therefore the Conditional Asham Offering needs to be more valuable than a Guilt Offering (Rema's own thoughts and Rabbeinu Yonah, beginning of Brachos).