Counting analysis (isolating the effect of the levels of a single attribute on choice, or the joint effects of multiple attributes on choice) would indeed be biased if the other attributes within the same concept or across concepts (but within the same task) are somehow not balanced and orthogonal (independent in variation).
But, our CBC designs (assuming you don't do any prohibitions, and that you use enough versions of the design--and 4 to 10 versions are often enough) are near-balanced and near-orthogonal. So, the presence of any level is (across all concepts and tasks for the sample) accompanied by essentially equal presence of all other levels of all other variables. This makes it possible to isolate the effect of each level on choice under assumptions of main effects (for example) or first-order interaction effects (as another example).
MBC should also (asssuming you follow similar design principles) be equally unbiased in Counts.