Extended x-ray absorption fine structure has been measured at the K edge of copper in CuScO(2) and CuLaO(2) to investigate the local origin of negative thermal expansion (NTE) along the c axis. A positive expansion of the Cu-O bond has been measured within the entire temperature interval to be contrasted with the negative expansion of the distance between average atomic positions measured by diffraction; the inadequacy of the riding correction to diffraction data has been evidenced. The weak temperature dependence of the parallel mean-square relative displacement (MSRD) indicates a rather stiff Cu-O bond, while the large perpendicular MSRD measures an intense relative motion of copper with respect to oxygen atoms perpendicular to the c axis. The comparison between the two compounds enlightens the relevance of the correlation of perpendicular motion to quantitatively explain the apparent NTE of the Cu-O bond.