I am not sure what instructions apply to the Strata 5, but, for the Strata 3, I believe that, if you are using a crossover built into your receiver, your choice is to connect the sub output of the receiver to the low-level input on the REL, or disable your receiver's crossover and connect your receiver's full-range speaker terminals to the high-level input of the REL.
Where the latter applies, the REL is filtering and probably attenuating the signal from the amplifier, and then amplifying it again. I agree. This seems an anti-minimalist approach that might work contrary to the goal of reducing coloration and timing error. I guess the proof is in the listening.
REL's explanation for the high-level connection is that it allows the sub to capture the "sonic signature" of the entire amplification chain, thereby keeping the "timing and timbre cues" consistent. This seems reasonable, assuming that the REL subwoofer doesn't do its own subtractions or additions to the sonic signature. But then why are there subs that don't take the REL approach but nonetheless sound good? I understand that, with many matters of audio design, execution is more important than theory. However, for the REL argument to be true, it follows that (1) all other subs sound inferior, or (2) there are compensation effects. That is, there are defects in REL subs that are not shared by other subs, with the result that the other subs sound as good (or better) than REL subs, despite the inability of these other subs to capture the full timing and timber cues of the amplification chain.