The gemara in Yevamos 109b says evil will befall those who accept geirim, implying that one should not accept converts to the Jewish people. However, Tosafos cites a gemara in Sanhedrin 99b that says that Avrohom, Yitzchok and Ya'akov should have accepted Timna to convert. Because they didn't she went and married Eisav, resulting in Amalek who caused major problems for the Jews. To reconcile these two sources, Tosafos says that it depends on how adamant they are about converting. When they are adamant about converting, we must accept them, but otherwise they should be rejected. Tosafos then questions the actions of Hillel in our gemara, how could he convert these three converts who aside from making ridiculous requests were not pushing hard for conversion? Tosafos answers that Hillel was confident that in the end they would be גרים גמורים, as it turned out. But how does this answer solve the problem? They weren't pushing hard for conversion so why did Hillel accept them? It seems that Tosafos understands that pushing hard and being adamant about converting - מתאמצין להתגייר, has no essential value. Rather, there is always suspicion that a convert is not intending to keep the mitzvos properly, and therefore we must reject them. However, when they are adamant about converting and don't take no for an answer, or when the beis din is confident that they will keep mitzvos properly as Hillel was, they should be accepted for conversion.
Tosafos both 109b and 24b seem to understand that Hillel actually converted these converts prior to their acceptance of all the mitzvos, based on his confidence that he will be able to win them over. However, the Maharsha in our gemara explains that Hillel merely accepted them on the conversion track, but did not actually convert them until they accepted the mitzvos. He actually derives from here that if a goy comes to study Torah for the purpose of conversion, we are allowed to accept him.
Rashi also seems to understand like Tosafos that Hillel actually converted them immediately. However, Rashi makes things a little confusing because Rashi writes that Hillel was confident that they will ultimately accept, but also writes that the ger who denied torah sh'bal peh, wasn't considered a kofer because he believed in torah sh'bal peh, but didn't believe it was from Hashem. Why isn't Rashi happy saying simply that Hillel's confidence was sufficient to accept them as geirim even though they weren't yet keeping mitzvos? Rashi seems to understand that had they been labeled as kofrim, Hillel would never have had the confidence that he can win them over to be geirim gemurim. But, Hillel realized that they didn't deny the mitzvos of torah sh'bal peh, they were just missing the education necessary to realize that it is from Hashem, therefore he was confident that after educating them, they will accept.
Rav Moshe (Dibros #81) has another approach in understanding Rashi. The ger believed in Torah sh'bal peh and accepted to fulfill it, but he didn't believe that the p'sakim of the chachamim of his generation qualifies as Torah Sh'bal Peh. Since conceptually he accepted, he is only lacking in education, not belief or acceptance to do. Therefore, Hillel was able to accept him. However, Rashi is still bothered that although Hillel may accept him, since he doesn't qualify as a חוץ לדבר אחד, he shouldn't accept someone who won't keep all halacha properly, to which Rashi answers that Hillel was confident that in the end, he will accept. According to this approach the right to accept this ger was not due to Hillel's confidence that he will in the end be shomer all mitzvos, but rather because his rejection was only of the chachamim of his generation caused by a lack of education.