What it really meant when people talk about living fossils etc is that the morphology of the creature has changed very little. Genetically and on a cellular level there would definitely be a lot of changes from their earlier forms millions of years ago. DNA just doesn't stick around for more than a couple hundred thousand years maximum it seems so it's difficult for us to chart those changes that aren't visible in morphology. Creatures that seem to not change drastically in such long scale time usually have niches and environments that haven't changed drastically in their existence.
Well put. Although on the outside, a creature may seem not to have changed in any recognizable way, mutations nevertheless accumulated in its DNA with each generation. That's why we probably should avoid to use the term living fossil.