Have people who say "blood is thicker than water" experienced abusive, neglectful or distant families?

I find, especially here, that a lot of people feel that family members are "naturally" the ones you can trust the most, the ones who will always be "there" for you, people whom you can always stand by, whom you have to stay close to no matter what they have done... etc. In my family, I would never be able to take care of my mother if she got really sick because she closes everyone off and actually asks that people don't email her because it is too "hard" for her to "deal with". When my dad died, I could not get any extended family members to care about coming to the memorial service I organized. Friends have been much more "there" for me. This is not about my whining, but I wonder - can people who put family first fathom that not all families even WANT to be close?