I also thought the whole clamping action loosened when adjusting one side. But it actually has a feature that will allow loosening one side without loosening the other. Between the two clamps is a spring and a nut. If these are installed correctly, the clamps will perform like this:
The side with the nut will only loosen the clamping on its side
The side with the spring will loosen the clamping action on its side and also the angle adjustment.
The clamp becomes much more useful and much less irritating when set up this way. I only know this because it worked correctly on one of several of these clamps I have. All the others loosen the clamping action on both as you state. But with the nut solidly installed in one of the clamps, it behaves correctly. Of course, there are no instructions about this nor is there anything to tell you how to be sure the spring and nut are installed correctly.