I think some of the confusion around Aaron's examples arise from the fact that they are really two different kinds of scenarios :
1. We are looking at a single causal link, and looking at relationships at a specific moment in time. (examples 2 and 4)
2. We are looking at the existence of a causal link in time (photon traveling) and positing the possibility of reciprocity. (examples 1 and 3)
Symmetry of the first type always exists, but not of the second type - simply because the hypothetical causal agent does not have the capacity to effect what is needed. For example, if I reflect photons and can see, I can confirm 1, but being a man I can never reciprocate 4 - I cannot give birth to my father. Symmetry of the second type requires universal properties.
Here is my badly drawn attempt to explain the difference between Aaron's two principles :