the shiur of bal yera'eh (I)

Last week we mentioned the chiddush of Rashi (Sukkah 27b) that to be considered a part owner of a sukkah necessitates having a share worth at least a perutah. R’ Scheinberg in his Mishmeres Chaim (vol 1 in inyanei pesach) quotes the following question from the Imrei Binah (I could not find it, but I did not have the patience to wade through all his pilpul and really look): why do we assume the shiur to violate bal yera’eh is a k’zayis? Since the definition of ownership according to Rashi is controlling a perutah or more in value, even if a piece of chameitz is a k’zayis in size, so long as it is worth less than a perutah in value one should not be considered its true owner.

Rav Scheinberg gives two answers and my son and I (joint effort) think there is a third. More to come bl”n.