Half-Heusler semiconductors satisfying 18-electron rule typically display promising characteristics for thermoelectric applications. A persistent inconsistency between the type of charge carriers in some of these alloys as obtained from experiment and theory however casts serious doubt on the computational prediction of new and efficient half-Heusler alloys. To gain insights into the origin of this disparity, we have investigated the effect of intrinsic point defects on the electronic structure of four frequently studied half-Heusler alloys of the form XYZ with Y being Ni or Co. Using state-of-the-art ab initio calculations, our study reveals that interstitial Ni and Co are energetically most stable point defects in these alloys. Remarkably, interstitial defect modifies the location of the Fermi level inside the band gap as well as the value of the band gap, thereby bringing in close agreement with the corresponding experimental result. This work thus highlights the decisive role played by interstitial defects in thermoelectric half-Heusler alloys, which may open a new avenue for deliberately utilizing these defects as a strategy for tailoring electronic structure and hence the corresponding thermoelectric properties.