At the end of the day, why couldn't R' Yehoshua pick a case in which: Someone came to the yesomim on his own (without a kid) and said "Your father lent me and i paid back 1/2" In which case R' Eliezer would agree its Meishiv Aveida, and he wouldn't have to swear. And the Seifa would also make sense meaning "But if the yesomin (even a katan) are tovea then he's not believed"? The Gemara seemed to not answer its original question. Thanks.
This question is one that bothered many of the great Acharonim, see Maharshal, Maharsha, Maharam Shif and P'nei Yehoshua. The P'nei Yehoshua says that since Rebbi Eliezer Ben Ya'akov does not excuse the Meishiv Aveidah due to a Migu (see Rashi DH v'Rebbi Eliezer) the Gemara could not ask that the Tana should write our Mishnah according to Rebbi Eliezer Ben Ya'akov, since the Mishnah is coming to tell us rules of Migu. See also the aforementioned Achronim for alternative suggestions.