Poor Man's Korban

In the mitzvah(#123) of korban עולה ויורד, the Chinuch says ואם הוא עני והביא כשבה או שעירה לא יצא ידי חובתו. והטעם לפי שאחר שרחם האל ברוך הוא עליו ופטרו בכך אינו בדין שידחק עצמו להביא ביותר ממה שתשיג ידו. ובזה יקנה כל מבין עצה לבלתי עשות הוצאות ביותר מן הראוי לו לפי ממונו, יען כי בו סבה לגזל את הבריות כשמבקש למודו ואינו מוצא.  The Minchas Chinuch (#11) asks this contradicts a mishna in Negaim (14:12) that a poor person can fulfill their obligation by offering the korban of the rich person?  The Sfas Emes Yoma (41) defends the Chinuch by differentiating between the korban of a metzorah vs. that of the olah v'yorad.  When it comes to metzorah, as the Torah describes in the beginning of the parsha, the poor man's offering replaces the chattas and olah animals with birds.  There, the mishna says the poor man can fulfill his obligation with the rich man's offering for they korbanos are the same.  However, regarding the olah v'yorad, as the Torah describes in Vakikra 5, the rich man brings a chattas but the poor man brings both a chattas and an olah.  Since, the poor man is obligated in those two korbanot he can't fulfill his obligation by merely bringing a chattas like the rich man. 
The Minchas Chinuch (#17) says its unclear from the Rambam and Chinuch what is the definition of a poor man vis-a -vis the עולה ויורד; do we say its like tzedakah it depends if s/he had 200 זוז or maybe if you can afford the rich korban that already makes you obligated?  The Achronim point out that it is clear that the measuring stick of wealth in this situation is if the person can afford the animals as is מדיוק in the Chinuch who says  ועשיר נקרא לענין זה כל זמן שיש לו, that is if he can afford the korban he is called a rich person.  This is also clear from Rambam and Toras Kohanim (see Avi Ezri Shiggugos (10-:13.)  [If so, how can there be a case of the poor man bringing the rich man's korban if he can't afford it?  See Chazon Eish Negaim 13:13 that gives a scenario.]
The Panim Yafos (14:22) suggests that a metzorah who can afford one animal is obligated to bring that one animal as the chattas and the olah will be a bird offering. We see he also assumes rich/poor in this context is if the individual can afford the korban.  However, his words are a big chiddush one would naturally assume that the birds and animals are distinct sets (see also Briskor Rav Maaseh Korbanot 14:2) and can't be mixed and matched (Michas Avrohom Yoma.)