The attached pic (stolen from the Classic Parts website, but listed for 51-55.1 trucks) has a hole near the upper end (arrow), but IIRC there was no screw there on my truck, just the two toward the bottom. There's no screw from the outside edge of the door that would go thru that hole, and screwing one in from the inside of the door would be very difficult. And I didn't install a screw there. There's an upset around that upper hole which is basically a standoff from the partial channel in the door. The fact that Classic Parts lists it as only fitting the trucks with wing windows surprises me. Not sure the earlier trucks would have the same channel.
The service manual doesn't differentiate between early or later (wing window) trucks on the door latch removal.

[on edit] The second pic is from a GM filmstrip that Brad Allen posted on his Flickr page.
HEREIt shows a different style channel guide for the earlier trucks. And it does mention the third screw, accessible from inside the door assembly. So the mystery of the difference between early and later trucks is solved. The two lower screws are horizontal on early doors and vertical on later doors.