The incompatibility thesis asserts that quantitative and qualitative research paradigms are inherently different from each other. Their irreconcilable differences prevent the possibility of a mixed-method approach.
It would be silly to maintain the impossibility of mixing perspectives when one has techniques that are equally examples of both. Take Fisher's Q-methodology, for instance: http://en.wikipedia.org/wiki/Q_methodology.
The Q-Methodology seeks to identify the predominant themes in a population's subjective view of an artifact or subject in a mathematical way that measures comparative agreement with various statements.
Since you get data on statements, it is necessary to take a qualitative view to select statements that might indicate differences in perspective and to combine related statements into representative threads.
But you are relying upon a quantitative technique to judge the subjective levels of agreement, since no one can pretend to objectivity in determining that. Your attitude infects others, and if different perspectives are not represented side-by-side as expressed by their own advocates, your own preferences can be subtly expressed in ways subjects may discern.