If we as main stream Americans from a European background look at the way Asian American parents relate to their children, we of course call them tiger or helicopter parents. But that is part of the culture and it can not be denied that this kind of attention has turned out young people who achieve in school and in the world.
The only reason we think Asian American parents are too strict is because we are not strict enough. That's why a lot of teens do drugs and have sex at a young age. If we were a little more strict the teens would be scared of getting in trouble and wouldn't dare try sex or drugs.
The greatest problem in answering this question is the question itself. It assumes that all Asian Americans are one homogeneous group of people when that is, quite frankly, not the case. I'm sure it's accurate to say that some Asian American parents are too strict on their children, but the same can probably be said of many American parents in general. Some parents apply more or less stricture to their children as they feel culturally and individually appropriate and I have seen parents of all races in America that are too strick, as well as those from all races that are too slack.
No, I do not believe that Asian American parents are too strict. I believe that Asian American parents understand that children need to be prepared for their adult lives. I also believe that American parents are too lenient on their children and this is why some of them turn out the way they do and the same for Asian American children.
Part of Asian culture, especially in China and Japan, is about hard work to get ahead. Chinese and Japanese students go to school year-round because there is no tradition of a summer break to help out on the farm. Asians tend to work harder to get ahead rather than spend a full month on vacation as Europeans do. In these respects, Asian American parents are hard on their kids but only because of a more tradition-based background.
I do not believe Asian American parents are too strict on their children. Parents have the right to choose how they raise their children and if anything Americans tend to be too lax on their children so saying that Asian Americans are too strict is probably biased by their own experience, which maybe it's not wrong, but it certainly doesn't make other methods wrong.