Short gamma-ray bursts may originate from the merger of a double neutron star (NS) or the merger of a black hole (BH) and an NS. We propose that the bright X-ray flare related to the central engine reactivity may indicate a BH-NS merger, since such a merger can provide more fallback materials and therefore a more massive accretion disk than the NS-NS merger. Based on the 49 observed short bursts with the Swift/X-ray Telescope follow-up observations, we find that three bursts have bright X-ray flares, among which three flares from two bursts are probably related to the central engine reactivity. We argue that these two bursts may originate from the BH-NS merger rather than the NS-NS merger. Our suggested link between the central-engine-powered bright X-ray flare and the BH-NS merger event can be checked by future gravitational wave detections from advanced LIGO and Virgo.