Well to be fair to HTV, when you look at the before and after you see that they DID do a very faithful recreation of the original shots.
But no one wants "faithful recreation of the original shots".
They want the effects to look modern.
I would say that HTV was faithful in that it looks like 1980s compositing work in HD. They did not improve upon the original techniques, nor did they try. Effects were blurry, light passes were misaligned, overall lighting was poor and fake-looking, and matte lines were visible. The only improvement HTV made was making the effects 1080p from 480i. In some ways, HTV's work was worse than the original effects work in 1988.
CBS-D was faithful, but brought the techniques into the 2010s. What they pulled off looks as if it was shot today.
HTV used "faithful representation" as a crutch. CBS-D used it as a challenge.