Let's look at this from a different angle. Here are the two positions under question:
1. Common ancestry.
2. Two independent insertions at the same base.
As it happens, there are ERV's that we can use to test these hypotheses. In chimps and gorillas we find multiple insertions from the PtERV family of retroviruses. Interestingly, insertions from that retrovirus are NOT found in humans and orangutans. Our two different positions make two different testable hypotheses in this situation.
1. Common ancestry. Since these insertions are not found in the human or orangutan genome, then these insertions must have happened after the chimp lineage split off from the human lineage. If they occurred before this point then they would be found in the human genome. If they occurred at the root of the ape tree, then they would also be found in the orangutan genome. Since they are only found in the chimp and gorilla genomes, this means that they had to occur independently in each species. Therefore, PtERV insertions in the chimp and gorilla genomes should NOT be found at the same location in the chimp and gorilla genomes.
2. Two independent insertions at the same base. If the specificity of retroviral insertion causes ERV's to occur at the same position 99.9% of the time (the rate needed to produce the shared ERV's between the human and chimp genomes), then we should find PtERV insertions at the same location in both the chimp and gorilla genomes.
As you can see, the two positions make the exact opposite prediction. Here is the data:
"Within the limits of this BAC-based end-sequencing mapping approach, 24 sites mapped to similar regions of the human reference genome (approximately 160 kb) and could not be definitively resolved as orthologous or non-orthologous (Table S3). We classified these as “ambiguous” overlap loci (Figure 3). If all 24 locations corresponded to insertions that were orthologous for each pair, this would correspond to a maximum of 12 orthologous loci. The number of non-orthologous loci was calculated as 275/287 (275 + 12) or 95.8%. This is almost certainly a lower-bound estimate owing to the limitation of our BAC-based mapping approach to refine the precise locations of the insertions."
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1054887/
The limits of the BAC-based method allow you to determine if two insertions are within about 100k to 200k base pairs of each other. Of the 287 PtERV insertions, 95.8% were not even within hundreds of thousands of base pairs of each other. Already, the independent insertion hypothesis is entirely busted. The authors of the paper then looked at existing genome sequencing to determine if the ones that were close to each other were actually at the same base. They couldn't find a single unambiguous orthologous PtERV shared by chimps and gorillas.
The common ancestor hypothesis is completely supported. The independent insertion hypothesis is thoroughly falsified.