It is a normal part of all herpesviruses to be quiescent. They have the capacity to reactivate from nothing but their genome into a fully functional virus.
Ebola is a negative-stranded RNA virus, and it is unlikely to find naked RNA in any body site. Rather, it is a mix of infectious virions and noninfectioius virus-like particles. The NEJM study you site was a qRTPCR only study. There was no attempt to actually culture the virus from the semen. Previous studies have tried culturing, and it difficult to culture semen-derived virus at the qRTPCR titers identified here.
Maybe confusingly, herpesviruses may still contribute to the biology of the cell even in the latent state.
DNA/RNA sequencing is also more sensitive in some ways (which can be both good and bad). It is also a very broad tool. You can go back to large datasets and try to squeeze more information out--even things you werent looking for originally, like herpesviruses. NCBI also hosts a very large repository of raw sequence data (SRA--the sequence read archive). Much of this data has decent metadata, so you could conceivably even do a new study on somebody else's old data.
An unusual example, but it's common to have Ebola virus RNA in semen (a fluid from another immuno-privileged site) with no detectable virus for months after primary infection. (https://www.nejm.org/doi/full/10.1056/nejmoa1511410 among others.) Similar patterns exist for lots of other viruses.