The intrinsic higher-order correlation of intensities which gives a measure of "pure" correlations among photons (corresponding to multiphoton bunching) is investigated with regard to ghost imaging with thermal light. The synchronous detection of the same light field by all reference detectors, which is a necessary condition for achieving an Nth-order ghost image based on N-photon bunching, is discussed. Furthermore, it is found that the enhanced high visibility of Nth-order ghost imaging is a consequence of the contribution of N-photon bunching, which is not a small value but is equal to the sum of all contributions from (N-1)-photon bunching. These results differ from those obtained by certain other groups.