It's a bit more complex than simple stereotypes.
Kaepernick is an athletic QB who has trouble making good reads, so did Vick.
If they were slower, white QBs with that issue they wouldn't be "heady," they'd be "unemployed."
There are a number of factors involved, some are racial, but other are incentives:
1) an athletic black QB will often play in college systems that employ his athleticism, and will be recruited by those coaches, conversely, a coach running a pro style system might prefer a strong armed, less athletic QB who'll be less tempted to use his athleticism and will go through his reads. There are athletic white QBs, such as Rodgers who played in pro systems, but Steve Young was an athletic white QB who had the same problems as the "stereotypical" black QBs until he sat on the bench in SF for a few years and learned how to play QB.
2) college coaches make a lot of money to win, and not develop QBs, so if they have an athletic QB, they'll often simplify the scheme so he can use his athleticism, not have to make complex reads and contribute immediately - this is optimal for the coach who may only have the player three years, but not for the QB if he wants to play in the NFL. It also means a lot of college QBs these day have mediocre arms but great athleticism and don't know how to play out of the pocket.
3) However, the rise of the spread offenses has caused most college QBs to come out with bad fundamentals, while the read option has increased the value of athleticism in QBs. So what was once a black stereotype has become an issue with almost all college QBs. One reason Eagles went gaga over Wentz, and not just his size, athleticism and arm strength, was playing in a pro style system even though it was 1-AA football, he had to adjust to a faster game, but they could gauge his "football intelligence" and ability to go through his reads.
Self-selection has an impact, let us say your a black QB with a big arm and great athleticism, coaches will sell you on being the "hero," in a scheme where you can go and make plays, and you may pass on Stanford and Alabama, where you'll play out of the pocket, hand the ball off a lot, and be told to run only in emergencies. It's more fun to play QB for Auburn, but better for your NFL career to play for Stanford.