I am reading here, page 5 that d' (d-prime) does not vary with criterion (in contrast to hit rate for instance which does vary with criterion, and which can be a biased measure of a subject's perception).
However, if we think of a subject that always answers "yes" when asked if a stimuli was present, even if not, then clearly the subject has a very liberal criterion (a negative criterion in particular), and it will follow that her hit rate = 1 but also her false alarm rate = 1, leading to a sensitivity of zero.
This also makes me wonder how sensitivity can be inferred independently from criterion. Let's assume that the subject has a d' = 1, i.e. their internal representation of signal and noise are distinct w.r.t. means of the distributions. However if the subject does chose to nevertheless use the very liberal criterion and always answer "signal present", we will be only able to infer that their sensitivity equals zero.
In summary, criterion seems to clearly impact sensitivity. Hence, why are criterion and sensitivity often discussed as being independent?