We attempt to explain a puzzling long-tailed peak shape of the X-ray absorption spectrum of the oxygen molecule in the energy region around 539 eV taking into account the Rydberg-valence and vibronic couplings. The long-tailed feature is found to arise from two dissociative sigma* states and the sudden drop in intensity is related to decrease in transition dipole near the crossing point between the repulsive sigma* and weak 3s Rydberg states with the quartet ion cores. This is supported by numerical wave-packet simulations allowing for all interchannel couplings between the Rydberg and valence manifolds with the quartet and doublet ion cores in a diabatic representation of the core-excited states.