The point being missed is that the discussion leading up to this statement in Romans 6:7 is about baptism, not about literal dying. The only "dying" that is being referred to is Jesus' death and the baptized believer's symbolic death by means of baptism.
When a person gets baptized as a disciple of Christ he, in effect, shares in Jesus' death and resurrection. The act of going down into the water is comparable to dying. And coming up out of the water equates with resurrection to a new life. This is the necessary being 'born of water' that Jesus mentioned in John chapter 3.
Jesus' death has power to cover over sin, and the act of faith that is involved in the believer's getting baptized allows him/her to share in the benefits brought about by Jesus' death and resurrection.
When Paul says that 'he that has died has been acquitted of sin,' he is referring to the living disciple that has been baptized. The term "acquitted" (or "justified" or "declared righteous") would not normally be appropriate when referring to a dead person. But since a baptized disciple is someone who has symbolically "died," its use by Paul is appropriate here.
That is not to say that a dead person won't benefit by Jesus ransom. The ransom makes possible a future bringing back to life of dead people. Otherwise, such a person would stay dead as the wages of sin. But such a resurrected person will afterwards have to exercise faith in Christ in order to be "declared righteous" and continue living. But Romans chapter 6 is not discussing the resurrection of dead people.
Thus, in connection with non-disciples that have died, it is not their death that "acquits" them, it is the ransom that will temporarily 'release' or 'free' them from what would otherwise be an unending sentence of death. However, if one accepts the ransom provision as a given, then one could say that 'death acquits,' since it would lead to benefitting from the ransom as far as a resurrection is concerned.
From the Society's standpoint, the problem they have is that they say the discussion in Romans 6 about baptism only applies to the 144,000. This is why they never use this chapter when discussing baptism. The WT maintains that only the 144,000 are "declared righteous." Everyone else is only 'declared righteous as friends of God' (Which is one big mumbo-jumbo, distorted lie - but I guess they have to come up with something for everyone else.)
Incidentally, in connection with the verb dikaioo (Strong's #1344) which appears in Romans 6:7, The Linguistic and Exegetical Key to the Greek NT says about its use in Romans 6:7, "To justify, to declare to be in the right. Here the word means either to be declared to be free from sin or to be acquitted from sin."
I might add, it was Romans chapter 6 that led me to understand what the "scrolls" of Revelation 20:12 were.
