What you personally suspect is neither here nor there - what matters is which interpretation is supported by the evidence. As you probably know, anthropoid primates all have the same genetic defect that causes a lack of the L-GLO enzyme, preventing them from synthesizing ascorbic acid. In this case, the hypothesis that the common defect is a result of common descent - inheritance from a common ancestor - is supported by what we already know about common descent through cladistics and the fossil record. What evidence is there to support the hypothesis that this common defect is actually the result of multiple discrete events, occurring in each and every species that exhibits the defect?
The conclusion of common descent is built into the bare assumption that the lack of the L-gulano-g-lactone oxidase gene is a "defect", or "nonfunctional" version of a gene that was purportedly functional at some point in human history. But even if that could be proven to be the case, it says nothing about nothing about whether it descended from a universal common ancestor or was a descendant of many independently created organisms or was itself created independently. In fact, the very (claimed) persistence and identifiability of these supposed pseudogenes millions of years after they supposedly ceased functioning could indicate that they have some as yet undiscovered function; (why else would they persist for so long?) It simply cannot be said definitively at this point that these types of genes have no function. In short, NDT can accommodate this evidence but it can also accommodate it's absence, which doesn't say very much for the utility of this alleged prediction of common descent.
Cordially,