Endogenous retroviral insertions as evidence for evolutionary relationships among primates
The Yohn et. al. (2005) paper (from Evan Eichler's lab) is describing a single type of endogenous retroviral element (loosely think of it as a 'species'), called PTERV1. They show that there were multiple independent infection events that resulted in permanent integrations in the ancestors of modern species (~3-4 MYA in the ancestors of gorillas and chimps, ~1.5 MYA in the ancestors of baboons and macaques). This in no way contradicts the notion of common ancestors among the apes/monkeys; indeed, they state this as a given in their analysis (emphasis mine):


  A total of 275 of the insertion sites mapped unambiguously to
  non-orthologous locations (Table 2), indicating that the vast majority
  of elements were lineage-specific (i.e., they emerged after the
  divergence of gorilla/chimpanzee and macaque/baboon from their common
  ancestor).


The presence of an ERV (or intron, or any general genomic synteny), can be used as evidence to support a particular model of common decent. Changes in genomic architecture are stochastic processes, and the work you cite by Li et. al. (Lynch lab) is showing us that ERV placement can occur at a similar, or nearly identical, location at a much higher rate than previously thought. We therefore need to take this into account then calculating how strongly a shared ERV increases our confidence in a given phylogenetic model. 

The video you linked to uses a completely random (i.e., very simple) model of ERV integration, setting the chance of an insertion at a given location at 3.3e-10. The findings by Li tell us that this is incorrect. In daphnia, at least, ‘hotspots’ may account for nearly 25% of new intron gain. The video also failed to include all of the instances of ERVs that are not shared between humans and chimp (back-of-napkin, this could account for differences of ~0.3% between their genomes, see Mun et al. 2014). This will increase the probability of an exact match occurring by chance (e.g., put two people in a room, what’s the chance of them having the same birthday? Put 100 people in a room, what’s the chance of any of them having the same birthday?). 

So, let’s be extremely conservative and say that the chance of the same insertion at a given location in both chimps and humans is one in one thousand (1e-3, seven orders of magnitude more probable than in the original model). Sixteen shared ERVs are identified in the video; if each is considered an independent event because of no shared decent, we are still looking at odds around 1e-48 (1e-3 ^ 16). An alternative could be that they are derived from insertions that predate the split from a common ancestor. Given Li et. al., maybe each event should be given a probability of only 0.75 instead of 1.0 (as per the video) because up to 25% of them could be from hotspots. In this scenario, the probability is 0.01 (0.75 ^ 16). Therefore, the second hypothesis is 46 orders of magnitude more probable than the first. In my mind, this is extremely compelling evidence that humans and chimps share a common ancestor, using only ERV data. 

I want to be clear, I am fudging these numbers extensively towards not supporting common descent. The real odds will be much higher in favour of common descent.

For further reading, Welkin Johnson wrote a comprehensive review on ERVs in 2015 (paywalled, so you may need to search for Alexandra Elbakyan's scientific literature retrieval method if you don't have institutional access).



References

Johnson WE. (2015). Endogenous Retroviruses in the Genomics Era. Ann. Rev. Virology. doi: 10.1146/annurev-virology-100114-054945

Li W. et al. (2009) Extensive, Recent Intron Gains in Daphnia Populations. Science. doi: 10.1126/science.1179302

Mun S. et at. (2014) Chimpanzee-Specific Endogenous Retrovirus Generates Genomic Variations in the Chimpanzee Genome. PLoS One. doi:  10.1371/journal.pone.0101195

Yohn et. al. (2005). Lineage-Specific Expansions of Retroviral Insertions within the Genomes of African Great Apes but Not Humans and Orangutans. PLoS Biol. doi: 10.1371/journal.pbio.0030110