We are not trying to recover anything. My wife's old phone synced perfectly fine with this iTunes library (and my phones always have). The question is why can she all of the sudden not sync with this library. She has never been synced with a different iTunes library (for instance, on another computer), so there seems to be a problem with either iTunes reading the phone or with her phone. My phone does not have this problem and syncs just fine with this iTunes library.
If the answer is that iTunes (or the phone) has a problem and the above is the only way to fix it, then I guess it is what it is. Just seems silly given that her old phone synced without issue.