Who is rumored to have killed Laius?
This is a complex question, because you can examine this question from several different perspectives.
The city in general believed that Laius was killed by robber on the road. That is the official story, even if no one really could confirm it. But based on what can happen during travel in the ancient world, this story was plausible.
When the plague hit Thebes and Teiresias was called in to give counsel, there was a new rumor or accusation, namely that, Oedipus killed Laius. Hence, from this perspective, the word was that Oedipus was guilty.
Oedipus, of course, thinks what Teiresias is saying is crazy and far fetched. Oedipus does not listen, and he begins to blame Creon. From this perspective, we can say that there is a new rumor. Did Creon do something underhanded? In short, there is confusion.
When the truth finally comes to light, Oedipus is found guilty.