The Mishnah, Y'vamos 10:4, quotes Rabbi Yosi as follows:
כל שפוסל על ידי אחרים פוסל על ידי עצמו, וכל שאין פוסל על ידי אחרים אינו פוסל על ידי עצמו
If I correctly understand the explanation of the רע״ב and ר׳ קהתי based on ר׳ יצחק נפחא in the Talmud, R. Yosi means this:
Suppose Aaron is married to Miriam, and her sister Leah is married to Baruch. Miriam and Baruch both leave the country and are determined to be dead based on testimony. (In the case of each death, either two witnesses inform the survivors and are believed, or one witness informs the court and the court declares the person dead.) Then Aaron marries Leah, but then Miriam and Baruch show up alive.
Well, if Aaron and Miriam were only kidushin-married, then we're afraid people will think that they weren't married at all (because the kidushin were based on a condition that wasn't met, for example) [and won't know about Leah and Baruch's marriage], and will thus think Aaron and Leah's marriage was valid. So we require Aaron to issue a bill of divorce to Leah, lest people think she can end a marriage without one. Therefore Leah cannot now go back to Baruch (because she looks like someone who's been married to another man, who cannot go back to her previous husband) and Miriam cannot go back to Aaron (because she looks like his divorcee's sister, which is a prohibited relationship).
But if Aaron and Miriam were fully married, then we aren't afraid people will think they were never married. Therefore, no bill of divorce as outlined above is necessary. Therefore, Leah doesn't look like Aaron's divorcee and so no one is prohibited to her previous husband.
If Aaron and Miriam were fully married, I don't understand why Leah can go back to Baruch. Back in 10:1 we say:
האשה שהלך בעלה למדינת הים ובאו ואמרו לה "מת בעליך" וניסת ואחר כך בא בעלה, תצא מזה ומזה
— that a woman who married based on incorrect information that her husband had died cannot go back to him. R. Yosi doesn't argue that point there (though he does argue another). Why can Leah go back to Baruch?