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I dug a little deeper into the CV code of CvBoostTree and CvDTree and I got a slightly different explanation:

• A weak classifier is indeed trained by minimizing some misclassification function (in case of Real Adaboost, its the Gini index, see: CV doc). So the wanted Hit-Rate does not come into play in this part of the algorithm.

• It then takes the best feature (lowest misclassification) and uses this one as the next weak classifier in the current stage.

• As the last step in this iteration, the algorithm calculates the overall stage threshold. And now the defined Hit Rate comes into play: the stage threshold is calculated so that the desired Hit Rate is guaranteed.
• In the next iteration, the weights are modified according to their classification in the last iteration step, therefore yielding different weak classifiers (decision stumps).

If you take all of this in consideration, it is clear that a HR of 1 and FA of 1 are possible!