Any single action revolver of the original Colt Single Action Army design can fire if the hammer is in the fully forward "rest" position, with a sufficient blow to the hammer. The original design has the firing pin mounted directly to the front of the hammer. The firing pin pokes through a simple hole in the back of the frame to strike the primer and fire the gun.
Modern designs, such as the Ruger Blackhawk and Vaquero, mount the firing pin in the frame rather than on the nose of the hammer. Between the hammer and the firing pin is a mechanism known as a "transfer bar". Its function is intuitively obvious from its name - it transfers the blow of the hammer to the firing pin.
This transfer bar is attached to the trigger. Unless the trigger is pulled fully to the rear, the transfer bar will rest below the firing pin, making no contact with it when the hammer is dropped. Pulling the trigger to the rear raises this transfer bar to a position between the hammer and the firing pin, allowing it to transfer the blow and fire the gun.
Below are some photos of the original Colt system and the new Ruger system (Ruger on top).
This transfer bar system allows the Ruger to be safely carried with six rounds in the cylinder. With the Colt, we only load five, leaving an empty chamber under the hammer.
When dropped, I swear these things are like cats - they always land "on their feet" or, in this case, the heel of the grip and the hammer spur. Guess what happens next?
So, yes, while technically the old design will fire without pulling the trigger, it takes a rather substantial blow to the hammer to make that happen. Since the gun was in Mr. Baldwin's hand when it fired, that would mean he would have had to have struck the hammer, like with the heel of his hand. An even more contrived, unlikely scenario...