Whether that can be a reflexive binding or not is governed by Chomsky's Principle A B or C respectively. Binding is related to scope (which is defined by c-command) where a quantifier (in the Lambda-calc sense) binds a variable-in the cases above the DP subject is quantifier that is binding a pronoun (a variable). The examples s/he offers however are incorrect (In all cases the subject is c-commanding the predicate), the issue becomes one of how that tree geometric structure is processed semantically (see Heim and Kratzer 1998). is correct in the sense that C-Command (specifically asymmetric c-command) is necessary but not sufficient condition for binding. C-Command is a tree-geometric relationship that describes two nodes relation to each other. There are a few concepts being conflated here.
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