The president of Atletico Madrid continuously insisted that they own all the rights to Falcao, but this simply isn't true.
Falcao is on a wage of 10M euro per year, and the return the investors wanted is 60M euro in transfer fee. This narrows down the list of potential clubs that can buy you out to very few. Atletico had no say in where Falcao goes, they had an option in the winter transfer window, but that expired. The owners needed their return and they were going to get it one way or the other.
The list can be narrowed down to PSG, Monaco, Real Madrid, Chelsea and City. City aren't making large investments any longer, PSG have their fix of strikers. Of the remaining three, it is apparent that Real Madrid didn't want to pay up the 60M + 50M in contracts for Falcao (for whatever reason). Apparently Chelsea matched the 60M clause but to pay Falcao the 10M per season in wages would involve a total gross salary of 300k+ per week, which just isn't manageable.
Chelsea also have the issue of not being allowed to directly purchase a player from a third-party owner (apparently this is what turned ManU off a move) so it would have required a two-step sale with Falcao going to one club outright and then to Chelsea. Apparently with the David Luiz transfer on the same day he moved to Chelsea Benfica bought out the entirety of his rights from third-party owners (so you can summize that Chelsea gave them the money to buy out that deal so that they could purchase 100% of Luiz directly from Benfica, thus avoiding the third-party rule in England).
With all of these factors you end up with only one target: Monaco. They have the 60M to pay out the investors, they have the funds to pay his wages of 10M per year and better yet they have no income tax so they don't have to supplement the gross.
So in the end Falcao is moved around Europe by his investors with the only goal of making a return for them. He has little to no say in his final destination because of a deal he agreed to years ago while he was still in South America.