Well i think people have a tendency to blame the ol' "grandpa was an alcoholic so thats why i am one" excuse. There is no doubt though that addictive tendencies and brains are inherited much like depression or anything else. In addition to genetics, environment plays a large role. Nature vs Nurture. Problem with that is, if your mom was an alcoholic and also raised you, is it the nature or the nurture to blame if you, too become an alcoholic...? What came first the chicken or the egg.
The fact though that no one in your family has addictive issues means one of two things: #1 it isnt always genetic and #2 just because they arent addicted to mind altering chemicals, doesnt mean that they couldnt have been. Perhaps they did not act on their addictive impulses.
My granfather was a major lush and so is my cusion. Im just a pill popper.