If A and B are somewhat confounded, then having B in the model as well as A can change the results.
See e.g. "Ambiguous Results in Functional Neuroimaging Data Analysis Due to Covariate Correlation," Andrade et al., NeuroImage 10, 483–486 (1999).
It's a general statistics issue, not just a neuroimaging one, of course. A similar point is made in _Applied Linear Statistical Models_, Neter et al., Fourth Ed., p. 294, in the section on multicollinearity.
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