Demai, Chapter 4, Mishnah 1. This mishnah presents us with a novel principle: there are times when a person may rely on the word of an am ha'aretz in matters of tithes.
The first case - asking the seller on Shabbos:
A person bought produce from an am ha'aretz, who is not trusted regarding tithes, and forgot to separate from it the required demai tithes before Shabbos. On Shabbos itself one may not separate tithes, not even demai tithes, so the buyer finds himself with no way out. The mishnah comes and teaches: he asks that same person on Shabbos whether tithes were in fact separated from the produce, and he may eat on the strength of his word.
Two reasons for this reliance:
The awe of Shabbos: On Shabbos an am ha'aretz is more afraid to lie than on any other day of the week, since his fear of sin is greater then, and as a result his trustworthiness and reliability are greater.
The pressing need of the moment: On Shabbos itself the buyer is in a bind, since he has no way to separate the tithes.
It is the combination of both reasons together that permits eating on his word.
However, the mishnah continues: once night falls at the conclusion of Shabbos, one may no longer eat the produce until he separates the tithe. This proves that the trustworthiness on Shabbos does not stand on its own. For if it were enough that he was asked on Shabbos and was believed on Shabbos, it would be permitted to eat on his word even after Shabbos. From here we learn that we are dealing with a combination of factors: the am ha'aretz's fear of lying on Shabbos, together with the pressing need that exists on Shabbos.
Asking a different person:
The mishnah continues: if the buyer cannot find the person from whom he bought, but rather another person who is also not trusted regarding tithes, yet knows something about the source of the produce, and he says that it has been tithed - he may eat on his word as well, by virtue of that very same principle, since the words were spoken on Shabbos. But once night falls at the conclusion of Shabbos, he may not eat until he separates the tithe.
Terumas maaser of demai that fell back into its place:
Another case: a person bought demai from an am ha'aretz, and he must separate from it maaser rishon, and from that maaser rishon take terumas maaser. What is the law if that terumas maaser fell back into the produce from which it was separated? The produce becomes meduma - a mixture of Terumah and non-Terumah. And amei ha'aretz are afraid of Terumah and of eating it; they regard it as a stringent matter, and it is something they are genuinely concerned about.
Therefore, if that am ha'aretz truly did not separate the tithe from this produce, then the terumas maaser taken from it is terumas maaser in every respect, and once it fell back in, this is a matter of grave concern even according to the view of the am ha'aretz himself.
For this reason Rabbi Shimon Shezuri says in this case, of terumas maaser of demai that fell back into its place: "Af bachol sho'alo v'ochlo al piv" - even during the week, and not only on Shabbos, about which we said that the fear of lying is greater, he asks him and eats on the strength of his word.
For if the am ha'aretz says that the tithe had already been separated from the produce, so that the separation of the tithe and the terumas maaser that followed were not necessary at all - he is believed. Because if he truly had not separated the tithe from it, that terumas maaser that was separated would have been necessary even according to his own view, and its falling back in would be something he himself would be concerned about. For this reason the buyer may believe him in this case that he did in fact separate the tithe.
In summary: In this mishnah we learned the cases in which one may rely on an am ha'aretz in matters of tithes: asking the seller himself on Shabbos, and asking another person who knows about the source of the produce - both by virtue of the combination of the awe of Shabbos together with the pressing need of the moment, and therefore once night falls one may no longer eat until he separates the tithe; and the case of terumas maaser of demai that fell back into its place, in which the am ha'aretz is believed according to Rabbi Shimon Shezuri even during the week, because the concern applies according to his own view as well.