1) A simple answer to this question is that the Amora'im of the Gemara did not always know all the Beraisos. In Ma'arava ("the west," or Eretz Yisrael which is in the west of Bavel) they knew the Beraisa about "Siman l'Davar" but they did not know the Beraisa about Bi'as Shimsho.

2) Another possible way of answering this question, which can hold true even if we say that the people in Ma'arava did know the "Bi'as Shimsho" Beraisa, is based on the explanation of the Vilna Ga'on. The Vilna Ga'on (in Bi'ur ha'Gra, Shulchan Aruch, end of Orach Chayim 261) learns the Gemara differently from Rashi. He learns that "Bi'as Oro" ("his light has come in") means that all the stars have come out (so the night sky has now received the maximum light). "Bi'as Shimsho" ("his sun has come in") means that the sun has set well below the horizon. When three stars can be seen, we know that the sun has set properly.

To summarize, "Bi'as Oro" means that all the stars have come out, while "Bi'as Shimsho" means that three stars have come out.

The Vilna Ga'on now explains the words of the Beraisa, "Siman l'Davar" ("a sign for the matter"). A "Siman" gives us a handy way of recognizing something. For example, we say on Seder night that "Rebbi Yehudah gave Simanim for the Ten Plagues: "DaTZaCh ADaSh B'AChaV". He told us, in short, the first letter of each Makah and this way we remember what all ten were in full. Similarly when the Beraisa here says "Siman," it cannot mean all the stars, because when they have all come out, it is not just a sign, but it is night; it clearly is equivalent to the middle of the night. But if "Siman" means three stars, this means we have an easy way of knowing that it is night even though this would not otherwise be obvious.

In this way the Vilna Ga'on proves that "Siman l'Davar Tzeis ha'Kochavim" means that when three stars are out, we can recognize that it is night. And this explains why Ma'arava chose to cite this second Beraisa -- because it states more clearly than the "Bi'as Shimsho" Beraisa that three stars are out.

3) Here is a different answer for why the people of Ma'arava did not want to learn from the "Bi'as Shimsho" Beraisa. This idea comes from the Maharsha. We have to start from Tosfos (2b, DH Dilma) who asks on Ma'arava: why did they prove it from a Beraisa? They should have proved it from the Mishnah in Nega'im (ch. 14) which says that he may eat Terumah at Bi'as Shismho?

(While my first answer to this question was that the Amora'im did not always know all of the Beraisos, we cannot say this about the Mishnah. The Amora'im were always expected to know every Mishnah. This is why Tosfos asks that Ma'arava should have proved it from the Mishnah and does not ask that they should have proved it from the "Bi'as Shimsho" Beraisa.).

The Maharsha answers the questioin of Tosfos. He writes that Ma'arava proved it from the Beraisa because the main issue in the Beraisa is reading Shema (after all, the main Halachah being discussed in the first chapter of Berachos is Keri'as Shema), while the main issue in the Mishnah in Nega'im is when one may Terumah. How do we know that the main issue in the Beraisa that Ma'arava cites is Keri'as Shema? This is because, later on this page, the Gemara cites the Beraisa in full and starts off by saying, "When can one start reading Shema at night?" and continues "Siman l'Davar Tzeis ha'Kochavim."

In the same way that the Maharsha says that Ma'arava cites the "Siman l'Davar" Beraisa rather then the Mishnah because the Beraisa is discussing Shema directly, unlike the Mishnah, so, too, we can answer your question, Marcus, that Ma'arava cites the "Siman l'Davar" Beraisa because it is discussing Shema directly, unlike the "Bi'as Shimsho" Beraisa which is discussing Terumah, not Shema.

4) Ma'arava preferred to cite a Beraisa from the beginning of Shas:

I saw an idea in the Pnei Yehoshua (which is actually not very different from what I wrote above in the name of the Maharsha but is slightly new), who comments on what Tosfos (DH Dilma) asks on Rashi: why did Ma'arava prove it from the Beraisa of "Siman l'Davar Tzeis ha'Kochavim" and not prove it from a Mishnah?

The Pnei Yehoshua writes that he does not understand why Tosfos found it preferable to cite the Mishnah rather than the Beraisa. The reason why Ma'arava cited the Beraisa about Tzeis ha'Kochavim is because this Beraisa appears at the beginning of Shas, in Berachos, while the Mishnah that Tosfos wanted Ma'arava to cite is in Maseches Nega'im, near the end of Shas. Since we are now starting Shas it is better to cite a Beraisa from the beginning of Shas.

I can say the same idea to answer your question. Ma'arava preferred to cite a Beraisa from the beginning of Shas rather than a Beraisa about Terumah which appears somewhere in the middle of Shas.

5) Tosfos (2b, end of DH Dilma) explains why it is necessary to cite the Beraisa that Ma'arava cited:

I posed your question, Marcus, to a Talmid Chacham who referred me to the end of Tosfos (DH Dilma; above I cited an earlier part of that Tosfos). Tosfos has a different explanation of "Bi'as Oro" and "Bi'as Shimsho" than we have seen so far. He writes that "Bi'as Oro" is an earlier time. It is the beginning of sunset, which is 5 "Mil" before the stars come out (presumably this means 90 minutes before Tzeis ha'Kochavim, since 1 Mil is the distance in which an average person can walk in 18 minutes), while "Bi'as Shimsho" means Tzeis ha'Kochavim. Tosfos calls the latter "Mamash" -- namely, that the sun has "really" come in (i.e., it has totally set), meaning the end, rather than the beginning, of sunset.

(We are touching now on the famous question of how long one has to wait after sunset until one knows it is night. The opinion of Tosfos is similar to the position of Rabeinu Tam, who says that one must wait longer. Above, we saw the opinion of the Vilna Ga'on, which seems to be the opposite of the opinion of Tosfos, as is well-known that according to the Vilna Ga'on Halachic night arrives a lot sooner.)

Tosfos concludes that if Ma'arava would not have cited the Beraisa about Tzeis ha'Kochavim, we might have thought that one can say Shema at the beginning of sunset, since we could have said that the first Beraisa means that Bi'as Oro is sufficient.

Marcus, thank you for your very interesting question!

Dovid Bloom