Here is a summary of findings by a paper which suggests that the vast majority of genetic counselors tend to err on the side of protecting a mother's privacy if her husband is not the father of her child. Here is an important point though:
It is much more likely that bringing up the possibility prior to testing will put the woman in the very position we are trying to protect her from. ... If, as I have suggested, the counselor plans to attempt to keep paternity but not personal genetic information from the man, it is probably better not the discuss the issue ahead of time.
The problem is pretty obvious, for autosomal recessive diseases like Cystic Fibrosis both parents need to be a carrier. There have been instances when "fathers" found out they weren't carriers, and that is how they discovered that their child was not their biological ...