Ok I can understand this behavior a little. I'm kind of a germophobe, and if I see someone coughing into their hand all match, I am not going to shake their hand after the match, I will just tell him that I don't want to get sick. I've done that a few times before. Also, if i am sick, or bleeding from my hand, which has happened a few times before from falling/diving, I won't shake my opponent's hand, and I will tell them why. I don't think this has been a big deal before for my opponents.
Which reminds me of a funny story. When I was first getting back into tennis several years ago, I played my very first Flex League match against an opponent that I didn't know at the time, and I didn't feel very well during the match. The next day, I still was not feeling well, so I went to the doctor. It turns out that I had strep throat, and I'm sure that I had it the night before during my match. So I sent an e-mail to this person who I only met the night before, saying that I just tested positive for strep throat, and it is likely that I had it and was contagious the previous night when we were playing tennis. So I told him that if he is showing any symptoms, that he should get himself checked out. That made me chuckle, lol.