Why use both high side and low Side diode-ORs for redundant power?
Why use both high side and low Side diode-ORs ... ?


It is to protect against all forms of misconnections (see below).
Linear Technology explains it in their Design Note 444.

It can be easily seen that removing one of both ORing diode pairs in Figure 4 will result in a short of one of the power supplies.
And in Figure 5 Battery A and Battery B would have been in series if there were only 1 ORing diode pair. (Worst case, the batteries would be shorted via the ground wiring.)