In AFM-based single molecule force spectroscopy, it is tacitly assumed that the pulling direction coincides with the end-to-end vector of the molecule fragment being stretched. By systematically varying the position of the attachment point on the substrate relative to the AFM tip, we investigate empirically and theoretically the effect of the pulling geometry on force-extension characteristics of double-stranded DNA. We find that increasing the pulling angle can significantly lower the force of the characteristic overstretching transition and increase the width of the plateau feature beyond the canonical 70%. These effects, when neglected, can adversely affect the interpretation of measured force-extension relationships. We quantitatively evaluate force and extension errors originating from this "pulling angle effect" and stress the need to correct the pulling geometry when stretching rigid molecules with an AFM.