I think that the parents of Olympians of very supportive of their kids who are competing for their country. They just want to see their kids be successful, just like any other parent in the nation. They back their kids in anything that they want to do, and are proud.
A common thread among successful Olympians is the strong support of family, who spend time and money helping them train to achieve their goals. Parents of Olympians must be knowledgeable and interested in their child's sport, but that doesn't make them overly competitive. Obviously, it takes a lot to maintain an elite athlete's mental and physical health and supportive families are integral.
Based on what I've seen in the Sochi Olympics, the parents of Olympians are very supportive. I can see them in the stands, cheering and shouting encouragement to their children. They have obviously traveled across the world to root for their kids, at considerable expense, I'm sure. And with all the warnings about terrorism, they're brave to make the trip.
Of course there are probably those stage mothers and fathers in the world of athletics too that push their kids beyond what they want to do but for the most part these parents just see what the children are capable of and like to do and support them in their many hours of practice and travel.
Parents of Olympians are overly competitive. They are usually the ones that instill competitiveness in their children. Kids aren't necessarily born with the desire to be better than other kids, but lessons from previous generations get instilled in them and making them interested in beating others. Parents of Olympians are perhaps more competitive than their own kids.