Do we always take the corner frequency of a filter at exactly -3dB?
It's not 3dB absolute, it's 3dB down from the peak, or some sort of nominal attenuation.  So in your case, where the passband is -3dB, 3dB down is at -6dB.
Note that some filters (e.g. Chebychev) have significant passband ripple; if this exceeds 3dB then the &quot;3dB down&quot; figure loses meaning.  In that case, or just if it's what matters to the system designer, a different definition of bandwidth may be chosen.