In the previous mishnah we learned that although the law of demai holds that we do not believe an am ha'aretz who claims to have separated tithes, nevertheless, if a poor person who is an am ha'aretz says that the produce in his hand came from the gifts to the poor - which are exempt from tithes - he is believed. The mishnah, however, qualified this: the credibility applies only to something that people would plausibly give to a poor person in that form.
Our mishnah spells out in which items the poor person is believed to say "these are gifts to the poor," and in which he is not:
Kernels: The poor person is believed to say that he received them from the gifts to the poor. But he is not believed to say "this flour was given to me" or "this bread was given to me," since gifts to the poor are not distributed as flour or as bread. The Rashash adds that if the poor person claims he received the kernels from the gifts to the poor and he himself ground them into flour or made bread from them, he is believed.
Rice: He is believed regarding rice that has not been processed. Some explain that this means rice still on its original stalk, and others explain that it has already been removed from the stalk but its outer husk is still on it. Either way, we are speaking of unprocessed rice, and about that he is believed to say it was given to him as gifts to the poor. But if he claims it was given to him after it was processed, whether raw or cooked, he is not believed.
Beans: He is believed to say that he received the beans themselves from the gifts to the poor, but he is not believed to say that he was given ground beans, or green beans that were crushed, which is a form of processing, neither when they are raw and certainly not when they are cooked. People do not distribute gifts to the poor in that form.
Oil: He is believed to say that the oil was given to him as ma'aser ani, since it was accepted practice to separate ma'aser ani after the olives were pressed and the oil was made.
Oil that comes from nikuf olives:
The stray olives left on the tree were designated for the poor, who would knock them down. "Nikuf" comes from the word for striking: the poor would strike the olive trees and bring down the last remaining olives. Regarding such oil the poor person is not believed to say that he made it from nikuf olives, because these olives are very few, and this is not the usual way to produce olive oil from them. Therefore, when he claims that the oil came from nikuf olives that he gathered together and is therefore from the portion of the poor, we do not believe him to exempt it from demai.
In summary: The poor person is believed to say that the product in his hand came from the gifts to the poor only when it is the way of that product to be given in that form: kernels, unprocessed rice, beans as they are, and oil. But regarding items that have undergone processing, such as flour, bread, processed rice and ground beans, and likewise regarding oil that comes from nikuf olives, he is not believed, and their status is that of demai.