Both arguments miss the point. One of the classic arguments for common descent with modification is "parahomology," or, as Darwin called it, similar structures serving dissimilar functions. The flipper of a whale, the wing of a bat, and the arm and hand of a human being show striking similarities in skeletal architecture, considering the very different uses to which these different forelimbs are put. Bring in the foreleg of a dog or cat, and the question arises: why should modifications of the same basic plan be put to such diverse uses -- especially when we have (e.g. in the inverted retina of the vertebrate eye and the "right-side round" retina of the cephalopod eye instances of dissimilar structures serving very similar functions)? Evolutionary theory answers this: parahomologous structures are opportunistic modifications of a structure inherited from a common ancestor.
"Vestigiality" is a subcategory of parahomology: it refers to cases where the most conspicuous function of a structure in most species that have it is lacked by some species. Now, "vestige," itself, does indeed reflect the conclusion that these structures are explained by evolution, but the basic observation does not assume common ancestry. You don't have to assume that a dodo shares ancestors with flying pigeons to wonder why it had wings at all, since it didn't fly. You don't have to start with the assumption of common hominoid ancestry to note the human plantaris tendon, and realize that in humans, unlike other hominoids, it doesn't enable us to clench our feet into fists (it doesn't even reach the foot bones). You don't need to assume that vampire bats had ancestors who ate solid food to note that some species have small, rounded cheek teeth where other bats have molars suitable for grinding food, and wonder what vampire bats need these structures for. Darwin called such structures "rudimentary" rather than "vestigial," and merely noted that they could most readily be explained as vestiges that had lost some of but rarely all of their functions. They can be defined and recognized without any reference to evolution or common ancestry (and then used as evidence of that common ancestry).
Indeed, the philosopher John Wilkins once pointed out, on the Talk.Origins newsgroup, that one could recognize vestigial structures in cases where evolution wasn't even a possible explanation for them. Consider the very reduced (in anatomical structure and function) limbs on many children of mothers who took thalidomide during pregnancy. These are clearly reduced in function compared to their obvious homologs in related individuals, yet they clearly have nothing to do with evolution (thalidomide is a teratogen, not a mutagen, and these children can have children of their own with normal limbs; the effects of the drug are not inheritable). But of course the point is that one can recognize vestigial organs in many cases where known mechanisms -- reproduction, inheritance, mutations that reduce function, genetic drift and natural selection -- can explain them, and do so better than any other explanation that has been offered: why else should such structures fall into nested hierarchies where other branches are occupied by species whose homologous organs have the additional, obvious function?
Of course, the author exhibits a small problem with understanding the classic mechanisms of evolutionary change. He asks:
What is the mechanism that leads to loss of function? For example, consider the appendix, which was classified as a useless evolutionary leftover (although its function has been demonstrated in recent years). Evolutionists have postulated that in the past, man had a larger cecum, but as man progressed from a higher-fiber diet to a lower-fiber diet, the larger cecum became less necessary. Thus the appendix is said to have resulted from a loss of cecal size. What is not explained is just how a change in diet would change the DNA—adding, subtracting, or modifying information—in order to bring about this structural change in man.A change in diet is not thought to have changed DNA. Random copying errors that went on all the time produced changes in the size and shape of the cecum. As the diet changed, though, changes that would once have been detrimental (because they left the mutant less able to digest food, hence less nourished and weaker) became neutral, perhaps even beneficial (since resources weren't being expended to build a large organ that wasn't necessary). A change in diet changed which variations were "fittest" and most likely to survive; it didn't create the variations directly.