Confusing "their", "there", and "they're" is simply an error. In contrast, saying "It was me who did it" can be the right thing to do in situations in which "It was I" would sound too formal or "awkward", as Jeri puts it. Most people know when to speak in a formal manner and when not, and how. However, there are cases in which rules are hard to find. I am often amused when I hear labour representatives talk about politics; in many societies, including British and Australian, they cannot possibly find an adequate language level.