As an athlete who competes at the top level of a sport and as a friend of 3 olympians, I can tell you that the athletes want to win. When the parents want the athlete to succeed more than the athlete, they end up peaking their career below the top level. The athletes who make it to the olympics are motivated by thenselves, and their parents don't usually tell them to do anything.
Of course there is not an objective answer as some will have some objections to my point. In America, most athletes would not reach the level they are at by simply a parents' push. They must love what they do to some extent. Yes parents probably push very hard on their children, but my father does the same for me with my schooling, and coaches do the same.
There is probably a small percentage of parents who do push their children when they are small, but this seems to me to be an ultimate path to failure if the child does not take over the interest in a big way. It doesn't seem to me to be fair to saddle Olympic parents with this stereotype, when in fact many of them willingly go through years of sacrifice in order to support their family member who truly has a love of the sport they choose.
From my experience most people performing in the Olympics are adults, but some competitions do favor a younger crowd. In these cases I believe the children are often committed although they do receive reinforcement from their parents. I don't think this is a bad thing especially if the child possess enough talent to make it to the Olympics.
I think it depends on the parents. As with other careers such as acting and modeling, you can get some sideline parents in sports. Those parents are usually trying to live vicariously through their children. But I don't think that any athlete makes it to the Olympic level without wanting to be there for themselves.
No, Olympic parents do not push too hard, because the children have to want it. With as much work as goes in to being at the level that you can compete in the Olympics, the child has to want to do the activity. If the child doesn't have the heart for it, they will never succeed to that level.