Answer

The Oral Torah had until then been transmitted orally, and it was forbidden to write it down. I assume that all these collections are editorial compilations that gathered the reliable sources that were accepted as Jewish law. But there were several editors, and they had different views (Rabbi Hiyya, Rabbi Oshaya, Rabbi Judah the Prince, and others). Some of the sources perhaps never reached them at all.
When they say that any teaching not found in Rabbi Hiyya and Rabbi Oshaya is mistaken, the intention is that it is hard to rely on baraitot that were not included in those collections. That does not mean they are all mistaken, only that there is greater concern about them. Therefore, if there is a difficulty for which no reasonable solution can be found, or a contradiction with a source that is included there, then the baraita should be rejected rather than the other source. But still, when such a baraita exists, it is part of the oral tradition that reached us and was not written down, and therefore it carries weight. Hence they try to examine whether it is nevertheless reliable and correct.