I missed something

This is kind of an old post, but in case you were still wondering, I'll try to help you out.

Well, Barbara had not seen Zip when he was supposed to interview her, he just called on the phone, so that's why she seemingly didn't recognize him, and why he changed his accent, his voice is the only part of him she would have been able to recognize.

However, towards the end Barbara explains that she actually used to know Zip, she was his secretary a few years ago and she made this plan up to get him to fall in love with her. So she actually had seen him before, she knew it was him all along, but you don't find that out until the end of the movie.