The Bartenura explains that the Mishna is talking about an ani and a ba'al bayis to state that even the mitzvah of tzedakah is not doche the issur of hotza'ah. But the klal of to'eh b'dvar mitzvah being pattur should make it impossible to have a hiyuv in the Mishna according to the Bartenura's explanation.
The Tana'im argue whether To'eh b'D'var Mitzvah is Patur or not. It could be that the Mishnah here is according to Rebbi Eliezer who holds that one would indeed be Chayav in such a situation (137a).
The TOSFOS YOM TOV himself suggests another answer, but REBBI AKIVA EIGER on the Mishnah (#3) rejects his answer.
lets stick to simple pashat look out the Rambam( Rishon) in Perus Hamisnayots that Ani and Bal Habyots is for simplicity ISAAC
Good. The Rambam's explanation is one of a number of explanations why the Mishnah used the terms "Ani" and "Ba'al ha'Bayis," and seems to be the simplest.