a) I don't understand why you still feel the need to cheat, when you are happily married. (present tense, may or may not cheat again)

b) I don't understand why you still felt the need to cheat, when you are happily married. (past tense, cheating concluded)

Given the two statements above:

"I don't understand why they still feel the need to (alledgedly) cheat, when they already have all the best manager and players" is grammatically correct, given that it is an ongoing investigation that has not yet been concluded.

* This ends the grammar element of this thread *