The problem cuts both ways.
It's true that many Asian-Americans are raised to be hard-working and disciplined at the expense of less tangible leadership-related qualities. Mainly, what I witnessed growing up in a very large Asian-American community was an overemphasis on quantitative measures of academic ability (grades, scores, etc.), an exceptional reluctance to question authority, and underdeveloped social skills. On top of that, there are also the two, constant nagging reminders from older Asians: (1) no matter what you do, you will look like an Asian and that's how the world will see you, so don't waste any time entertaining the notion of assimilating with more mainstream American culture, and (2) Asians are better than white people anyway, so don't degrade yourself. The result for most of us Asian Americans is a challenged relationship with the culture and society that surrounds us, a disbelief in our ability to succeed the same way white Americans succeed, combined with a dueling self-hate and superiority complex.
On the other hand, other Americans certainly do see Asian Americans a certain kind of way (hard-working, good at math, meek, and--most ludicrously and offensively--soulless). All Asians to them become a caricature, a collective whole without individuals worth distinguishing. This is, of course, unfair and racist, though many would struggle to rationalize that it's not the same as generalizing that blacks are violent, hispanics are lazy, or that Jews are penny-counters. Clearly, it's all terrible and makes it harder for indivuals belonging to such groups to be treated as individuals. For Asian Americans, this only reinforces the belief that we can never compete on the same grounds and should never bother reaching beyond doctor or engineer (lawyer if you're rebellious).
However, there is often a self-knowing hyprocisy and jealousy underlying such bigotry. Growing up, it did not escape me that the same white parents who denounced Asian American students for being soulless when they beat their own kids in school, sports, art, music, etc., secretly schemed to get their children in with very same Asian-exclusive Asian tutors or piano teachers who were spreading all the soullessness. My friends' parents were always asking my parents for their 'secret' and requesting that I help their kids study after school.
What came first, the impression or the reality? It's impossible to say and moot, as neither side is justified in its outlook.