I would be doubtful too, since FedEx Custom Critical does not own any tractors.
When Diane and I were new, it took a while to learn and understand the differences between the various divisions (operating companies, or "OPCOs" as FedEx calls them) and the various employment or independent contractor relationships they offer. Tossing fleet owners into the mix further complicates the picture.
To most people, FedEx is FedEx. Many are not even aware of the different colors the FedEx logo comes in to communicate the difference in operating companies. We often point that out to customers saying "We (Custom Critical) are 'FedEx Blue.'" Most people are surprised to realize that while they have been looking at the FedEx logos all their lives, they did not notice the different colors. (The "Fed" is purple in all logos. The "Ex" comes in different colors.)
If you question your friend further, it would not surprise me a bit to learn that he is one of the millions of people who looks as FedEx as one company instead of a large company with several divisions. For all we know, a FedEx Ground fleet owner may be trolling the school looking for drivers.