They are fake studies, and it is possible that HSV 2 could be in semen, but it is not common. If you read the study, you can see that only 3% of samples had HSV 2 in them, so 97% of the time it is not in semen and in the samples that were positive for HSV 2, 6 of 8 were collected from men who were having an outbreak at the time. Your question was about sperm carrying virus without an outbreak (asymptomatic shedding). So in respect to the article by Dr. Corey, this means that out of 256 samples, only 2 were positive for virus when no outbreak was present. This is what I meant by “rare” in my response above.