Eder and Ohta have found a violation of the Luttinger rule in the spectral function for the t-t'-J model, which was interpreted as a possible breakdown of the Tomonaga-Luttinger(TL) description in models where electrons can pass each other. Here we have computed the spin correlation along with the spectral function for the one-dimensional t-t' Hubbard model and two-leg Hubbard ladder. By varying the Hubbard U we have identified that such a phenomenon is in fact a spinless-fermion-like behavior of holes moving in a spiral spin configuration that has a spin correlation length of the system size. ; Comment: 3 pages, RevTex, 8 figures in Postscript, to be published in Phys. Rev. B (rapid communication)