I realize that your comment is specifically directed to her subsequent written statements, but it does raise an important issue with regard to Amanda's first written statement. Everyone agrees that the first written statement was false. Call it a lie or full of lies if you want. There are many different reasons for people to lie. Not all of them are entirely self-serving or evil.
My understanding is the first statement put Amanda, Rafaelle, and a 2nd male at the murder scene. The argument if favor of Amanda's guilt has always been that Amanda, Rafaelle, and a 2nd male were at the scene. The discrepancies between them concern the identity of the 2nd male and the details of what occurred. For many the key falsehood in Amanda's statement is the identity of the 2nd male. And that is what she was convicted of. Of course we do all agree (I think) that Patrick wasn't there and Rudy was. What possible benefit could Amanda have hoped to obtain by replacing Rudy with Patrick? Was she simply trying to protect Rudy? Why would she do that? Was she just trying to confuse the police? Throw them off the trail? Didn't she admit to being there? Wouldn't she have been better off saying that Rudy was there and she left before anything happened. If she did have guilty knowledge, what benefit would she gain from lying about the 2nd male? What benefit would she think she would gain from lying about the 2nd male. Wasn't she arrested immediately after giving the first statement? It seems that her lie didn't work out well for her.
From the view point of Amanda-is-innocent her statement and her "lies" make a lot more sense. Please take a look at the quote I posted above which has been attributed to Chief De Felice. He clearly spells out, from the Perugia Police perspective, what happened. Amanda denied any knowledge or involvement, the police didn't buy it, she "buckled" (suggesting she was under some pressure) and gave them a statement implicating Patrick (which the police "knew" was "correct"). The statement momentarily got the pressure off her but certainly wasn't in her long-term interest. Why did she implicate Patrick? I suspect given the texts between Amanda and Patrick and possibly other evidence that Patrick was already on the police radar. When she did name Patrick the police "knew" it was "correct". Why didn't she name Rudy? I don't think his name had come to the attention of the police at that point and she had absolutely no idea that he was involved. She wasn't there.
OK, she lied about Patrick. We all know that. But there is a long convoluted leap of logic from that to "she was involved in the murder of Meredith". It just doesn't add up.
In her subsequent statements it seems she continues to say that Patrick "might" or "could" have been involved in the death of Meredith. She had absolutely no idea that he wasn't involved. She wasn't there. And the police seemed to think he was. They "knew" it was "correct".