I disagree about it being too simplistic. I think quite the opposite to be honest. There's a reason why Aguero, Kompany, De Bruyne etc never wanted to leave and it isn't because City are winning trophies. We won trophies, players left, Liverpool won trophies, players left, same with Chelsea and Arsenal around the Vieira era (they were on a clear decline though).
Plenty of reasons why an agent might want to hide some of their earnings as well.
Wait, I see what you're saying about it being too simplistic. But I think it's fairly obvious it happens. They're hiding it well which means it isn't as simple as just transferring a couple tens of millions here and there, obviously. But I'm absolutely sure it happens one way.