The reason why a lot of people believe Murali chucks is because of incorrect arguing by Murali supporters. They always say that its a optical illusion that Murali throw and also says that he throw as much as anyone else but they all miss the fundamental reason why Murali doesn't throw.
Definition of a legal delivery from Cricinfo
3. Definition of fair delivery – the arm
A ball is fairly delivered in respect of the arm if, once the bowler's arm has reached the level of the shoulder in the delivery swing, the elbow joint is not straightened partially or completely from that point until the ball has left the hand. This definition shall not debar a bowler from flexing or rotating the wrist in the delivery swing.
Most people simply don't know what a throw is. To summarise the law, a throw is a straightening of the arm from a bent position when delivering the ball. Of course for most people, to prevent the straightening the arm is to bowl with a straight arm. However it is possible to bowl a legal delivery with a bent arm action as long as the bent arm doesn't straighten which is impossible for most people. The thing that makes Murali unique is that he is double jointed so he cannot straighten his arm fully. People say that this deformity allows him to break the law but that is untrue. His deformity allows him to bowl a legal delivery with a bent arm action which makes him unique from every bowler in history. Because of the misconception of the laws of throwing, people just look at the photo of Murali bowling with a bent arm and just assume he chucks. However the only way to prove he is chucking is to find a video of him bowling where his bent arm is straightening which I bet no one can find. In that sense there is no "optical illusion" because it is blatantly obvious he doesn't straighten his arm (as much as anyone else) when bowling.
Now the recent research about the throwing laws has shown that a straight arm from a person without a deformity is not exactly 180 degrees straight and that there is a slight angle in the arm. So when bowling there is a involuntary straightening of the arm. So that is why bowlers like McGrath, Pollock and Harmison chuck without us knowing it. There is a slight straightening of the arm from an already relatively straight position. With Murali, there is a slight straightening of the arm from a bent arm position but it is just as legal (or illegal) as the previous bowlers i just mention. So the research didn't really exonerate Murali because if people knew the action throwing laws there really shouldn't really be a case against him. The research just shows that every bowler involuntarily straightens his arm.
Thanks for reading