When I view the Open profile for Edward T Adams (the father), I see the same Father of ... [private daughter (1930s - unknown)] and [private daughter (1930s - unknown)] that you do, also with no active links. When I view the Open profile for Edward T Adams Jr (his son), I see Brother of [private sister (1930s - unknown)] and [private sister (1930s - unknown)], also no active links. This is what I would expect.
For the situation that I'm encountering, both profiles (parent and child) are Unlisted. I'm on the TL of the parent profile but not on the TL of the child profile. The parent profile is where I can see private info from the child: <parent> of given/surname with active link, which hovering over discloses the full birth date and birth location of the child. My expectation is that for the child, I really should just see: <parent> of [private <child> (decade - unknown)] with no active link. Since you're not on the TL of the parent, you can't view the parent profile.