In the semantics of the conversation, clearly Knox is contending with someone. There are basically two possibilities, about who is the second referent (or "actant"). Either she is contending with her parents about a version her lawyers suggested her (lawyers suggested her to not lie about the fact that she was at the cottage, and she tells this to her mother that there is no reason why she should lie - but the mother disagrees), or she is contending not against a person present there but against a theory which the police (or prosecution) is suggesting (she puts forward her argument against the police theory: there is no reason why I should lie).
In the first case, her parents are asking her to lie; in the second scenario, the phrase "I have no reason to lie" is merely emphatic, she wants her parents to believe her and puts forward an argument for that.
I bear in mind that Knox comes from a hearing before a judge (Matteini) where she decided to remain silent (she refused to answer questions, she refused to make statements; so she stuck to her ambiguous hand written notes) and she is elaborating the strategy about the defensive line she needs to keep at a coming interrogation by the public minister.
Indeed, the question about what her version could be is not stupid at all. She could be thinking of putting forward a recollection where she was at the cottage but she is innocent, something similar to her 05:45 spontaneous statement (I'm sure her lawyers suggested that was the best strategy). It might be indeed stupid to lie if she actually was at the cottage, which is what her lawyers believed.
But let's say that her parents said: no! And in order to convince her, they suggested that the police was lying, that their evidence fas false. Curt and Edda Knox wanted a hard line, because they agreed to that strategy under suggestion of a PR firma. The conversation betwen Knox and hr mother might be about this. I don't think this is stupid at all. Also because this resembles to what Sollecito's parents did with Raffaele: his father pressured him to keep some defensive line rather an another.