From that sentence there's no way to know whether the speaker believes they know the identity of the killer, or if the speaker knows who it is. They could be discussing potential suspects.
They were talking about who killed her husband.
You might think that it implies that they do know or that the speaker knows because it does not say who might have killed or who could have killed or who would have killed or who can have killed. However, speakers are not always as articulate as listeners might like them to be, and that speaker might have been referring to a discussion about potential suspects even though there is no modal in the verb phrase to express the notion of "possibility" as distinct from factuality.