Whoa, that seems a bit harsh! I think she's just afraid of being rude, which I think is completely understandable. Some people really take it to heart when people ignore their texts. Plus, she seems to like him, so she probably doesn't want to send him the wrong message of "leave me alone."
What I was going to suggest has already been suggested: wait hours between texts, and let him know that you're not a constant-texting kind of person. If that doesn't work, then... I don't know.