Hi. Welcome to the forums.
Regarding your questions, I first need some clarification. Does the participant know what exactly "A" is? Is the participant shown "A" before the experiment, so he or she can acquire a baseline? Or, is "A" something that common folks understand? Example of this: If "A" is Nike and "B" is any other type of sneaker, and we assume wearing Nike shoes is something everyone has done at some point, then one has a reason to identify "A" or not. Otherwise, a participant is calling out "A" and "other" indiscriminately.
Do you understand what I am trying to ask?
EDIT: I believe my question is answered in this line: '... but due to an experimental manipulation that we introduce we believe participants are able to intuitively identify above chance stimuli “A”.' My oversight.