The thing about personal statements is that most people are going to have very good personal statements. A personal statement can only be so good. Also lots of people essentially have their personal statements written for them or just straight up lie in terms of work experience/what they've read/things they've done. There is no way for universities that don't ask for interviews to check up on this as everyone is pretty much writing it.
This is why I believe that personal statements (and references to an extent) are no where near as important as people make them out to be. Sure they are good for showing interest in the subject and that you actually want to go for that degree, but there is no way they are anywhere near as important as hard evidence such as grades.