You understood that the Get is thrown into the courtyard while she is with her husband, but this is an incorrect understanding of the Mishnah. The Mishnah is talking about the Get and not about the husband, meaning that even if he threw the Get on a bed and she is on that bed, she is not divorced. Regarding this the Gemara says that if it were her bed, she would be divorced. See both the Tosfos Yom Tov and Meleches Shlomo.

The Meleches Shlomo supports this interpretation by citing a Girsa which does not have the word "Hu" in the Mishnah (but simply "Afilu Imah ba'Mitah"), and therefore it would definitely refer to the Get mentioned in the previous sentence. I checked the Parma and Kaufman manuscripts of the Mishnah and they also do not have the word "Hu" in the text, and similarly other manuscripts of the Talmud do not have the word "Hu" (although one did have the word "Hi," which would refer as well to the Get).

Yoel Domb

Indeed, also according to what I wrote in the Point by Point, the intent was that he threw the Get on the bed on which both were sitting. One might have thought that in such a case, he lends his bed to her, and she is divorced through this.

In any case, the wording of the Mishnah is a bit awkward -- first it discusses throwing a Get. "Imah b'Mitah" connotes that they were together the entire time. If he throws it, it should have said, "to the bed on which she sits."

Also, the word "Im" connotes a certain level of equality (like Chazal expounded "Im ha'Chamor" -- Am ha'Domeh l'Chamor). It is strange to say that a person is "Im" a Get.

I am still unsure about how other Mefarshim learned, but several explicitly say that the Mishnah means that the Get is with her, so we will fix the Point by Point (both on the Mishnah 77a, and the citation at the top of 78a) to say:

"[the Get] is with her on the bed."

Pesach Feldman