Humans can haptically discriminate surface textures when there is a significant difference in the statistics of the surface profile. Previous studies on tactile texture discrimination have emphasized the perceptual effects of lower-order statistical features such as carving depth, inter-ridge distance, and anisotropy, which can be characterized by local amplitude spectra or spatial-frequency/orientation subband histograms. However, the real-world surfaces we encounter in everyday life also differ in the higher-order statistics, such as statistics about correlations of nearby spatial-frequencies/orientations. For another modality, vision, the human brain has the ability to utilize the textural differences in both higher- and lower-order image statistics. In this work, we examined whether the haptic texture perception can utilize higher-order surface statistics as visual texture perception does, by 3D-printing textured surfaces transcribed from different 'photos' of natural scenes such as stones and leaves. Even though the maximum carving depth was well above the haptic detection threshold, some texture pairs were hard to discriminate. Specifically, those texture pairs with similar amplitude spectra were difficult to discriminate, which suggests that the lower-order statistics have the dominant effect on tactile texture discrimination. To directly test the poor sensitivity of the tactile texture perception to higher-order surface statistics, we matched the lower-order statistics across different textures using a texture synthesis algorithm and found that haptic discrimination of the matched textures was nearly impossible unless the stimuli contained salient local features. We found no evidence for the ability of the human tactile system to use higher-order surface statistics for texture discrimination.