I have heard the phrase “software first, then hardware” in some Rope Rescue classes, what does this mean, and is it important?

My experience with this phrase is with regards to the Tandem Prusik Belay; and specifically with the order that equipment would be rigged onto a carabiner.  In some areas, a pulley (PMP) and a Load Release Hitch (LRH), are a standard part of the Belay System, regardless of whether it is a raising, or lowering belay.  The theory here, was that no change to the belay system would be necessary when the Mainline function changed, thus making things safer.  The phrase was a reminder to place the tandem Prusiks closest to the spine of the carabiner for the strength; in the event of a failure, the tandem Prusiks would hold the load on the strongest part of the carabiner.  The PMP would be rigged atop the tandem Prusiks, thus, software first, then hardware.  Many practitioners have moved away from using a PMP on the belay, as it has demonstrated the ability to significantly loosen the tandem Prusiks.  This in turn causes the tandem Prusiks to perform unreliably, or fail altogether.  So, for many people, the phrase is obsolete if the PMP is not part of the Belay System.  The orientation of software and hardware is not usually an issue with a mainline, as the system is always under tension.  Depending on the situation, a compelling argument could be made either way for the orientation of the software and hardware on a mainline system; and I have seen problems arise from either orientation.