I don't believe we know the truth.
Here's what keeps me grounded on the theory that Robinson in fact did it....
He or someone looking just like him is caught on the roof, marching to the university, climbing stairs, etc. He was in fact there.
How would you get a patsy to sign up to be Robinson, if he didn't do it...was just a decoy? How would you find someone willing to suffer through prison, trials, then the death penalty? Robinson would have had to sign up for this in some way, to be a decoy. To go to the campus, to the roof, knowing he's being set up (you would think).
Seem unlikely you'd find a volunteer for that. Could he have been 'duped' into it? I don't know how, but anything is possible.