You have assumed that the headline figures for transfers are the amounts that the club receives. Agents' fees might come out of the figure paid (or collected) but not show up as such separately in the accounts.
From The Telegraph in 2002:
(http://www.telegraph.co.uk/sport/football/teams/aston-villa/3039091/Gregory-Ive-done-no-wrong.html)
"In May last year, Adam Crozier, then chief executive of the FA, told a private dinner that "agents and hangers-on" had pocketed £7 million of the £9.5 million Angel transfer fee. By then the FA were already looking at this transfer but, according to one insider: "The wall came down and we could find nothing."