Tosfos on daf 16a says that an Eved Ivri can acquire himself (i.e. go free) via a Shtar, but the Mishna did not mention this, since the Mishna only mentioned methods of becoming free that could be done against the will of the master.
This does not seem to fit in with the pattern of the previous or subsequent Mishnayos: the first Mishna mentions that a woman is "koneh atzma" via a Get, and the third Mishna mentions that an Eved Kenaani is "koneh atzmo" with a Shtar.
Tosfos did not base his assertion on an inference from the words "Koneh es Atzmo" (which would seem to mean that the Eved is the one activating the Kinyan) for, as you point out, this term can certainly include Kinyanim which are not done by the Koneh at all, but by the husband or master. (In fact, we see that the Gemara on Daf 2b offered other reasons for why the expression "Koneh Es Atzmah" is used in the Mishnah.)
Rather, Tosfos is simply suggesting that the author of the Mishnah chose for himself a limiting factor for what he mentions in the Mishnah. He chose to mention only the ways in which the Eved Ivri goes free against the master's will. (In a similar vein, the Gemara on 22b suggests that the Tana of the Mishnah there chose to only mention Kinyanim of an Eved Kena'ani that cannot be performed on Metaltelin.)