The gemara says that one does not have the right to grab money from a borrower to be zocheh for the lender, in a situation where the borrower owes to others, because although his action is a zechus for one borrower it is a chov for the other. Rashi in baba metziah says that if the lender would appoint him as an agent to grab from the borrower, he would be able to be zocheh for the lender even though it is a chov for others. Tosafos and the Rosh disagree that even if he is appointed by the lender and given power of attorney, he cannot take from the borrower when it is a chov for others. The primary argument of Tosafos is that zechiya is by definition shlichus [which means that it is an 'anan sahadi' that the lender would want him to be a shliach, and it is as if he was actually appointed by the lender explicitly], so what is the difference if the lender appoints him as his agent or not, since by being zocheh for him he becomes his agent. The Ketzos Hachoshen (105:1) explains that rashi must hold that zechiya is not based on shlichus, therefore rashi holds there would be a difference whether he would be appointed as an agent of the lender or just grab it from the lender on his own. He explains that zechiya according to rashi isn't shlichus, rather it is a gezeira hakasuv that for a zechus the grabber cans serve as an extension of the lenders hand. Based on this, the concept of zechiya is limited to a situation of an absolute zechus, meaning it is not a chov for anyone else. But, if the lender actually appoints him as a shliach, that would work even if it is a chov for others.
The difficulty with this approach is that rashi writes explicitly that zechiya works m'din shlichus - רש"י ט ע"ב בד"ה יחזור, וז"ל דקסברי זכות הוא לעבד שיוצא מתחת רבו לחירות וזכין לו לאדם שלא בפניו דאנן סהדי דניחא ליה דיהוי האי שלוחו להכי עכ"ל
Clearly, rashi holds that zechiya works based on shlichus, so how can rashi in baba metziah hold that there is a distinction between whether he was made a shliahc explicitly or not?
I would like to suggest that Rashi agrees that zechiya works through shlichus. However, the shlichus only begins once we have established that it is an absolute zechus. Only when there is an absolute zechus, are we able to then say that the "anan sahadi" would turn him into a shliach. In a situation where it is not an absolute zechus because it is a chov for other lenders, then the concept of zechiya doesn't begin to turn him into a shliach. But in a case where the lender appoints him as a shliach, he doesn't need it to be an absolute zechus to implement the shlichus since he was explicitly appointed a shliach.