My guess is your wife entered by land. If you enter Mexico by land, the back of your FMM needs to be stamped by immigration before you can leave by air. The airline staff will check for this stamp so they do not get fined for letting you leave without it. There is an INM window near the ticket counters at most airports for this purpose. INM should also really make you pay the DNR fee for the FMM (or ask for proof that you have already paid it) but usually do not check.

Did AM examine your wife's passport when she checked in or did she use a kiosk?

The only time I have had an issue with this was when leaving Guadalajara after entering via the Nuevo Laredo land crossing. I had checked in online and didn't check a bag so went straight to the gate. I waited to board until our group was called and was finally sent to the INM window after the gate agent saw I didn't have the all-important stamp. This made for a mad dash through the airport, to the INM, waited in line, got the stamp, back through security, and back to the gate at the latest possible moment since we were at a gate on the other end of the airport.

I learned my lesson. I always stop at the ticket counter for travel document verification. Checking with the gate agent when they open the podium for your flight probably would also be wise just to be on the safe side. These issues are easy to fix if they are caught early. Nevertheless, it's ultimately the traveler's obligation (and vested interest) to ensure compliance with immigration rules. The airline is acting as an agent of the immigration authorities and enforcing the applicable rules but they are not responsible for the outcome should a passenger miss their flight due to lack of compliance.

It would be helpful if the INM would inform travelers about this requirement when entering via land and/or leaving via air and/or have airside offices to make it easier to resolve these issues when the occur. But that probably won't happen.

I'm glad everything worked out well for your wife and her trip.