If she added her Gmail account on a new device after this year, she won't be able to get Gmail push anymore. Gmail removed that feature for accounts added to devices after a certain date. She will either have to manually go in and refresh the Mail app to view her email, or download Gmail from the App Store to receive push notifications.
Those are the same two settings I have and gmail is fetching just fine. I would erase the gmail account on the device and add it back again, then I would restart the device. Does this have the latest ios version?
BTW, Pushing mail has been changed by Google, but this doesn't affect fetching mail.
I know it won't push but shouldn't the phone fetch?
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I did delete it and added it back again and it still doesn't work. I told her to erase and set up the phone as new unless someone here had another solution. She is running iOS 7.