Perhaps the answer is as follows:
The Talmud immediately cites a beraita which discusses a Scriptural derivation for the time when terumah can be eaten:
כדתניא ובא השמש וטהר ביאת שמשו מעכבתו מלאכול בתרומה ואין כפרתו מעכבתו מלאכול בתרומה וממאי דהאי ובא השמש ביאת השמש והאי וטהר טהר יומא דילמא
as it has been taught: And when the sun sets we-taher, the setting of the sun is indispensable [as a condition of his fitness] to eat terumah, but the expiatory offering is not indispensable to enable him to eat terumah. But how do you know that these words 'and the sun sets' mean the setting of the sun, and this 'we-taher' means that the day clears away? It means perhaps: And when the sun [of the next morning] appears, and we-taher means the man becomes clean? — Rabbah son of R. Shila explains: In that case, the text would have to read we-yithar. What is the meaning of we-taher? The day clears away, conformably to the common expression, The sun has set and the day has cleared away.
We see here that there are two ways to interpret the verse. One way would have the time for eating terumah as nightfall, while the other would have it the next morning. By linking this law to the recitation of the evening Shema, the Mishnah automatically eliminates the second reading of the verse. It can't be that terumah can't be eaten until the next day, because the time for reciting the evening Shema obviously can't be the next morning. Thus, the Mishnah is not telling us the precise time for when terumah can be eaten; it merely points us to one of the two already known possibilities. Once we know which of the possibilities it is we can then apply that time back to the Mishnah as the time for reciting Shema.
(This answer is at least somewhat inspired by the Rashba's commentary on this passage, but I'm not sure if this is actually what the Rashba means.)
