Unlike an aluminum plane, you can check for cracks. For carbon fiber, based on my understanding, they need either X-ray or ultrasound to check for cracks on the composite material.
To answer the distinguished professor's concern regarding inspection of composite aircraft structures, yes these procedures can be conducted at airports.
In fact, x-ray, ultra sound and all other NDT inspection methods have been being conducted at airports for many decades. The bizjet shop I worked in at LAX had the equipment and trained personnel to conduct ultra sound, eddy current, dye penetrant and magnetic particle inspections. X-ray inspection was contracted to a mobile specialist company due to cost efficiency considerations, but could have easily been added to the repair station rating had there been more call for it. As it was, we provided some outstation services to airline customers, but they all saw to their own heavy mx at their own mx bases. After all, our specialty was business aircraft and doing contract airline line mx just a sideline rather than part of the core business plan.
The above mentioned NDT technologies used in structural inspections are completely mobile and could be transported to outstations along with the inspectors as needed. However it is extremely rare that such an inspection needs to be accomplished at an outstation. Structural inspections are normally accomplished during scheduled maintenance checks at a mx base. Field evaluations are normally only necessary in cases of in-service damage incidents. In these cases, visual inspection is normally sufficient to decide whether a temporary repair can be applied, or it is safe to ferry the airplane back to base, or whether further evaluation or repairs must be conducted in place. While all of the above is applicable to aluminum airplanes with limited composite components, I don't see composite structures being treated any differently with respect to where and when NDT inspections are performed.