In the Mishna we find that the people of Yerichos left Peiah on vegetables, and the chachamim protested. The gemara explains that there was a legitimate halachic argument between them. The issue was whether the leaves of turnips qualify as מכניסו לקיום which is one of the conditions to be chayev in peiah. The people of Yericho held that since it is able to be stored together with the turnip bulbs, it qualifies as מכניסו לקיום and is obligated in Peiah, whereas the Chachamim held that this does not qualify as מכניסו לקיום and is exempt from Peiah. Therefore, according to the Chachamim, the people of Yericho who were treating the turnips like Peiah and not separating Teruma and Maaser were causing the poor people to violate the prohibition of eating tevel, that is why they protested.
Rashi on the Mishna explains that the problem with what the people of Yericho were doing is that they were considering it Peiah when it reality it wasn't and causing the poor to eat tevel, as we explained. According to this approach, there is room for Tosafos question - Even if Peiah is not technically binding, it should be considered hefker which is also exempt from ma'aser, so it shouldn't be a problem of eating tevel (Tosafos answers that since they only allowed the poor to eat and not the rich, it didn't qualify as hefker). However, in explaining the story of בן בוהיין, Rashi explains it very differently. Rashi implies that the leaving of Peiah on vegetables was effective in exempting it from ma'aser because it assumes a status of hefker and hefker is exempt from ma'aser. The problem is not that they poor would be eating tevel, rather the problem was that by doing a ha'arama to make it hefker and exempt from ma'aser is not proper. The Maharsha points out that Rashi in the Mishna is not the same peshat as he offer in the story of בן בוהיין, whereas Tosafos understood the case of בן בוהיין to be exactly the way Rashi explained in the Mishna.
Why does Rashi explain the case of בן בוהיין to be such a minor problem and not as he explained by the אנשי יריחו that the problem is a more severe problem of eating tevel? It seems that Rashi understands that the case wasn't limited to turnip leaves where there was mistaken halachic justification, rather בן בוהיין knew that vegetables were exempt from Peiah, but was machmir on himself to make it hefer as if it were Peiach, as a chumra. His intent was to make it hefker so that it would truly be exempt from ma'aser, therefore the concern in the mishna of feeding tevel to the poor doesn't apply. Tosafos question also doesn't apply because the fact that it is effective in exempting from ma'aser by assuming a status of hefker is exactly the problem.