JimmyC: Someone mentioned this earlier, but it sounds to me like another device is configured with her mobile number as an iMessage contact. That's the most plausible explanation since an iMessage txt won't appear as delivered unless a device has actually received it. Your wife won't receive it in either format if it's going to another device.
Involuntary autocorrect in operation on mobile device. Apologies in advance.
profrink: As mentioned, I'd get her to log into her Apple ID account and have a look at which devices her phone number is associated with.
I had this issue when I moved from my to Nexus 4 and forgot to unregister iMessage specifically for that device. Other iOS users would message me and I'd never receive anything as it was still thinking I had iMessage (which technically as far as the system was concerned - I did).
I think removing the Apple ID account from an iOS device doesn't de-register the iMessage number, this may have changed now but there is definitely still a bug in certain scenarios.