I think that Livy's attitude towards the material is not constant throughout his narration of this story. I think that he takes a skeptical attitude towards the material when he talks about the parts of the story that sound more mythical. When he is talking about more human events he sounds more convinced.
For example, when Livy is talking about the conception and birth of the twins, he says things like "the tradition goes on to say" and he calls it "the marvelous story." He does not say "it is said" again until he is talking about the omens that were supposedly received by the twins when they were trying to decide where to build the city.
In between, all the events are stated simply as truth. Livy does not express any disbelief in those parts of the story.