I don't find it hard to believe at all mate. Remember, we're the club that once made players take Ryanair to save on plane tickets. Think we even made Soldado take a Ryanair flight over to sign for us, after paying 26m for him. Before the new training ground, we used to have no professional dieticians or cooks on staff, and Spurs Lodge used to be a pretty disorganized place iirc.
Iirc we also have just that one large bloke (Levy's son in law, I think?) doing player liaison, while these days clubs have dozens of people for that. Levy still sits at the training ground and eats with the players, and his idea of motivating a star signing is to give him a lecture about his A-levels. Iirc, we still don't have a dedicated sports psychologist on the team, and I'm still uncertain whether we have a dedicated set-piece coach or if it's just something Montgomery does in addition to his other duties. We had our physio head in charge for something like two decades straight (or close to it), while other teams constantly refresh their physio teams to keep abreast of the latest developments in sports science. On transfers, we had our transfer chief admit he hated having to work in January, one of the three months of the year he's legally permitted to get deals over the line. And when Paratici arrived, he was apparently shocked at the lack of data science personnel we had on the scouting team.
Even on things like Spurs Play - until recently, we had that one interviewer bloke who's been at the club for twenty years straight doing all the interviews, while these days clubs have huge media teams of hundreds of people to manage every aspect of it.
Everything behind the scenes speaks to the club being run like Levy ran it in the late 2000s, and considerably behind the cutting edge. It seems to me like the priority is more to run Spurs like a homely family than a cutting edge institution.
So why would it be surprising we leave details like player flights to the players themselves?