Yes, they've verified this in several ways, either test-retest (ask for a variety of synesthetic associations and verify them some time later) or even by constr

Yes, they've verified this in several ways, either test-retest (ask for a variety of synesthetic associations and verify them some time later) or even by constructing challenges that would be easier for synesthetes than non-synesthetes for example, detecting a shape in a mixed cloud of numbers based on associated hue (much like some color-blindness tests).