Why is queen elizabeth II against harry taking a DNA test?

i'd bet my last penny that there is not a drop of royal blood in 'prince' harry..the queen did a thumbs down on harry wanting a DNA test..is she afraid of the truth? if its the waste of money..i'd gladly send them a few hundred pounds..why do these people shuck from truth and reality?...yeah..yeah..the Spenser's have redheads in the family...but he doesn't have those weird eyes like his uncle 'champagne charlie' or his peculiar Spenser aunties