For some reason, this website is blocked at work, so I can't read the context. But I tend to agree that improper usage of me and I are annoying. The reason I would read the context first, however, is that if the author is writing conversation, then I think it's obviously OK to imagine what your character might say, independent of whether it's right or wrong. But if this is a first person narrative about an experience, by a professional (and likely read by an editor) then certainly, shame on them.
I agree, b_b, context is important. It is a long article talking about how she grew up in New York, left, then went back to achieve literary fame, and how New York isn't cool anymore. Considering that at least part of the time she lauds her credentials and her success on the literary scene in NYC, it seems to be a more formal approach as opposed to a casual forum, say, like Hubski. Her writing style is mostly elevated and, well - I'd call it strong but I think there is room for improvement. She could learn how to edit herself, for one. Guernica, the site, appears to be an online lit mag of some sort so I would assume she would have to have her piece approved by an editor.