Halliday & Matthiessen (2014: 338n):
The account of lexical ergativity has sometimes been supported by reference to pronominal case marking in English. But this is also a mistake; pronominal case marking is not a feature of the experiential system of transitivity but rather of the interpersonal system of mood: the non-oblique (‘nominative’) case is used for Subjects in finite clauses and the oblique (‘accusative’) case in all other environments (including Subjects in non-finite clauses). It is thus related to arguability status, not the transitive model of transitivity.