At the top of Niddah 18a, Rav Huna explains the Baraisa as no machlockes, but two different cases. Isn't this a big dochek, that a Baraisa has two opinions, but they don't speak about the same case?
Kol Tuv and Yasher Koach for all your good work as we approach the big siyum!
Meir Eliezer Bergman
Manchester UK
To answer this question, I think we may use the answer that the Gemara sometimes offers, "Midi Gabei Hadadei Tanya" (see, for example, Shabbos 18a). That is, when there are two Beraisos we do not necessarily need to assume that they were stated together, but rather the Beraisos may be totally independent of each other. Consequently, there is no reason to assume that they are talking about the same thing.
The Gemara in Bava Basra (end of 93b) cites a Beraisa "Tana Rav Ketina" which suggests that Rav Ketina is a Tana in his own right. Therefore. it is possible that in our Gemara, Rebbi Chiya and Rav Ketina stated two Beraisos without even being aware of what the other one said. They both used the term "blood found in the Prozdor," but since there are different parts of the Prozdor it is possible that they were referring to blood found in different places. We should also remember that there is a principle of "Talmidei Chachamim Marbim Shalom ba'Olam" -- Talmidei Chachomim increase peace in the world, so whenever we have an opportunity to avoid a Machlokes, we do so.
In the light of the above, I do not think it is farfetched to say that Rebbi Chiya and Rav Ketina are talking about blood found in different places.
(In addition, I notice that the Gemara here says "Rav Ketina Omar" and not "Tana Rav Ketina." This suggests that Rav Ketina merely said it, but it was not actually part of a Beraisa. It may be that here this is not a Beraisa with two opinions.)
Kol Tuv,
Dovid Bloom