First and most importantly, what you point out here is that the science here is falsifiable. In other words, were the conclusions false, they would be demonstrated false by exactly the sort of finding you noted; an identical HERV-K LTR insertion in an orthologous locus that did not fit the pattern of descent with modification. it would seem a excellent area of exploration by “ID Scientists” if there actually were such a thing. But there really is no such thing as “ID science” so no such research has been performed.
It would, in fact, only take one such discovery to dismember the argument. And further, it would not even require a look that far afield taxonomically. The same primates examined in the originally paper could have served that had a single one of the HERV-K LTR insertions violated the pattern. And yet, none did.
Yes... the “- proof as well as + proof” that you ask for was pursued by the authors of the original paper. They found only the +.
The ERVs provided two independent but mutually supporting sources of information. Their relative age was determined by the accumulated point mutations. Their pattern of distribution among the primate species was independently identified by actual sequencing. Had they not been genealogically inherited, then there would have been no reason for them to have also correlated perfectly in both time and distribution with the branching sequence of the phylogenetic tree.
Certainly, if another explanation was in the offing, some of the insertions should have been shared by (say) orangutans and humans, but not gorillas. That would have been just as powerful a falsification as finding a recent insertion shared by humans and cave bears. Such insertions were actively looked for.
Yet none were found.
I can assure you that in the decade since this study was published, no contradictory evidence of the sort you describe has been found or published, and thousands of species have been sequenced in the interim.