As I understand it, the motor should not tilt up or down if it is equipped with hydraulic tilt and trim. The older outboards had a mechanism on the pivot bracket which "grabbed the tilt pin when the engine was shifted into reverse. That prevented the motor from tilting up when in reverse.
I've looked at my boat and motor. There is no such device. Even if there were, there would be no tilt pin for it to "grab". The motor must be held in place by the hydraulic piston so that it will not tilt up when reverse is used. If the motor can rock enough to drop the fork from the trailer, there has to be some problem in the hydraulic system, be it a seal, valving, etc. [I agree with this thought, a hydraulic system problem could cause movement]
Mine is even closer to horizontal. There is no way that can put significant upward thrust on the motor. When the trailer encounters a bump in the road, the boat and trailer are compressed together. That would put no force into the transom saver, unless you want to count the possible tiny bit of compression of the carpet on the bunks. Now, when you run over a pothole, the boat will tend to separate from the trailer. When that happens, the transom saver if secured at both ends, would try to draw the lower unit down. But since there is not solid connection between the saver fork, and the trailer roller, all that happens is that the fork separates a bit from the trailer roller.
When the boat drops back onto the trailer, that gap between the roller and the saver fork closes, and the downward thump is absorbed by the transom, not the saver.
I've wondered if the boat was lifting off the trailer; but the weight of the boat gave me doubts. I would not be surprised to find that the transom tie-down straps stretch somewhat.