The Mishna (Terumot 7:5) says:
שְׁתֵּי קֻפּוֹת, אַחַת שֶׁל תְּרוּמָה וְאַחַת שֶׁל חֻלִּין, שֶׁנָּפְלָה סְאָה תְרוּמָה לְתוֹךְ אַחַת מֵהֶן וְאֵין יָדוּעַ לְאֵיזוֹ מֵהֶן נָפְלָה, הֲרֵי אֲנִי אוֹמֵר, לְתוֹךְ שֶׁל תְּרוּמָה נָפְלָה.
If there were two baskets, one of Terumah and one of Chulin, and a Se'ah [specific unit of volume] of Terumah fell into one of them, but it is not known into which it fell, I can assume that it had fallen into that of the Terumah.
This case is strange because usually teruma, which is forbidden to be eaten from the Torah, should be treated strictly in a case of doubt.
My question is: What is the logic for being lenient when we don't know which basket the teruma fell into, based on the assumption it fell in a particular way, against the general rule to be strict with regard to a doubt in Torah law?
This is a summary of my research so far, which I put here so as not to distract from the main question:
Some commentators (Tosafot Yom Tov quoting Rambam Hilchot Terumot 13:13-14, Tif'eret Yisra'el) avoid the question by saying that the case is dealing with teruma in this time, which is prohibited to eat from the rabbis (derabbanan). If it were dealing with teruma prohibited from the Torah (de'orayta), it would not be permitted to assume the teruma fell into teruma.
However, it seems that this Mishna is necessarily dealing with teruma de'orayta. The Tosefta (6:10) quotes the same law in the name of Rabbi Yosi. Rabbi Yosi holds teruma is forbidden from the Torah at all times (Yevamot 82b).
Furthermore, the Peney Moshe (Mar'e Happanim 7:3 ד"ה רבי שמעון בן לקיש) says that the Tosafot Yom Tov misunderstood the Rambam, which was his source for saying this case is teruma derabbanan. The Rambam only meant to say it about the case of two things falling into two boxes, not one thing falling into two boxes. That would mean the Rambam takes the case of this Mishnah to be from the Torah.
In fact, it is Rabbi Yochanan (Yerushalmi 7:3), who is the one holds that teruma is still forbidden from the Torah (Yevamot 81a), who says that we are dealing with a case where there isn't a majority of chullin to nullify the teruma, which doesn't allow us to use the proportion of the mixture as a way to make the case permitted from the Torah (according to which there needs to be a majority of chullin).
Possible starting point: Yevamot 82b defends Rabbi Yochanan (in a slightly different case) by saying that this concept ("שאני אומר") is different, but it doesn't explain the logic why it should be different.
This question might also apply to Rabbi Eli'ezer's opinion (Terumot 5:2-6), but there are differences: the concept of safek is less prominent there, his opinion has both lenient and strict ramifications, and the sages disagree with him.