Court of Law has to prove beyond any doubt, the FA is able to use logic and reasonable deduction in their findings, it's not a criminal court.
The only thing that stopped the CPS from being able to find Terry guilty is the fact part of what Terry said before "you f##king black c##t" was obscured from view because another player ran past the camera. The FA are able to take other evidence into account and find whether or not Terry's defence is likely.
They deemed it "improbable, implausible and contrived" and also deemed Ashley Cole's statement as "evolution of Ashley Cole's evidence" noting that it was changed at a later date to further help Terry's case.
In short, the pair of them were politically correctly called liars. The legal courts couldn't 100% prove it, the FA doesn't have to go beyond reasonable doubt, they just have to prove it was likely to have happened.