hefker and the ptur of pe'ah from terumah and ma'aser

Pe'ah is exempt from any obligation to take terumah and ma'aser, but why that should be so is unclear. Rashi (Bava Kamma 28a) explains that pe'ah is hefker and all hefker is patur from tru"m. Tosfos rejects this possibility. The Mishna tells us that (acc. to Beis Hillel) hefker must be accessible to all, both rich and poor, but pe'ah is free only for the poor to take. Tosfos instead explains the ptur based on a gezeiras hakasuv. Kohanim and levi'im receive tru"m because "ain lo cheilek v'nachalah imach", they receive no portion in Eretz Yisrael. Since even kohanim and levi'im share the same rights to pe'ah it as everyone else, they have a "cheilek v'nachalah" and the reason for tru"m does not apply.

Recall that the Ketzos understood (according to the Rambam and Rashi) hefker to be no more than a type of neder by an owner not to use his property. Hefker creates a chovas hagavra to allow others access, but in no way changes the item itself, which is still considered in the owner's possession. R' Shimon Shkop (Sha'arei Yosher 5:23) points out that Rashi's explanation of the ptur of pe'ah seems to directly contradict the Ketzos. Why should the owner's chovas hagavra based on hefker exempt produce (which is still in his possession!) from the obligation of pe'ah?

Perhaps one might offer a bit of defense for the Ketzos. Perhaps the ptur from pe'ah is not dependent on everyone having actual rights to the produce b'poel, but merely the option b'koach to exercise the right to take the produce.

For those who want to dig a little deeper, basic pshat in Rashi and Tos here is hard to understand. Tosfos, at least in its hava amina, and certainly Rashi, seem to introduce the idea of hefker as an independent ptur from tru"um without a need for the additional gezeiras hakasuv of "ain lo cheilek v'nachala". Yet, Tosfos' themselves (Bava Kama 69a) note that the only reason hefker is exempt from ma'aser is because everyone has an equal right to take it, meaning the reason of "ain lo chelek v'nachala" is inapplicable. The ptur of hefker is not an independent din, but is based on the same gezeiras hakasuv Tosfos arrives it in their conclusion. Still don't have a good explanation for this point.