Yes, that's my interpretation of "probably, yes", and that's probably correct. (That fits the context, doesn't that?)
Another interpretation is: その顔 refers to Peter's face, 女の人 refers to women in general, the subject of してほしい is also women in general (same as 女の人), and the target of してほしい is Peter. (Peter had an expression Peter thought women in general would hope him to have.) Grammatically, this is also possible.