I don't think I did it by analysis ... but from the experience of having seen many such problems before.
The way to think about it is to reconstruct the question as an answer for each of the possible constraints. eg. for A.
A force in x is present between the block and the rod with the force P.
Now consider if that is true or false ...
The trouble is that I'd have got it right before you started asking questons, which suggests that I'm doing it from experience rather than evidence.
The answers seem to be saying that there is no constraining force in z, and no constraining moment in z. Which is OK for the force but clearly silly for the moment since the block cannot rotate about the z axis (there's a ramp in the way.)
That would be your objection right?
OTOH: what the diagram says to me is that there can be no net force in the z direction and no net moment about z. There can be net force/moments for the other two axis because of the slope... for instance, if the block can, in principle, rotate about the normal (to the slope) axis ... this would give it moments about x and z, but not z.
A "constraint" in this question does not stop motion, just limits it.
So, if I have this right, the question asked is pretty much the opposite of what you thought it meant.
BTW: thanks for forcing me to think about this.
