Re: "Inadvertently misrouted." Wow, that's what I call a spectacular display of contempt.
Yeah, FedEx doesn't use bulk carriers to save pennies... They are an airline all to themselves. They and UPS truly have huge operations the world over. UPS does use Kalitta Air as a sub contractor (i.e. if they have an extraordinarily large load that would need two planes whereas Kalitta happens to have a 747 in the area that can handle everything in one gulp), FedEx for the overwhelmingly large part does not contract out.
It's DHL that's the courier company that has a lot of partner/contractor airlines that provide metal in DHL colours to shift parcels around the world. They're part of Deutsche Post (have been for a while), and they're happy to not have overwhelmingly large infrastructure around when others have it already and it can be contracted for the appropriate capacity.