Indium phosphide colloidal quantum dots (QDs) are emerging as an efficient cadmium-free alternative for optoelectronic applications. Recently, syntheses based on easy-to-implement aminophosphine precursors have been developed. We show by solid-state nuclear magnetic resonance spectroscopy that this new approach allows oxide-free indium phosphide core or core/shell quantum dots to be made. Importantly, the oxide-free core/shell interface does not help in achieving higher luminescence efficiencies. We demonstrate that in the case of InP/ZnS and InP/ZnSe QDs, a more pronounced oxidation concurs with a higher photoluminescence efficiency. This study suggests that a II-VI shell on a III-V core generates an interface prone to defects. The most efficient InP/ZnS or InP/ZnSe QDs are therefore made with an oxide buffer layer between the core and the shell: it passivates these interface defects but also results in a somewhat broader emission line width.