Interlayer excitons (IXs) in MoSe2–WSe2 heterobilayers have generated interest as highly tunable light emitters in transition metal dichalcogenide (TMD) heterostructures. Previous reports of spectrally narrow (<1 meV) photoluminescence (PL) emission lines at low temperature have been attributed to IXs localized by the moiré potential between the TMD layers. We show that spectrally narrow IX PL lines are present even when the moiré potential is suppressed by inserting a bilayer hexagonal boron nitride (hBN) spacer between the TMD layers. We compare the doping, electric field, magnetic field, and temperature dependence of IXs in a directly contacted MoSe2–WSe2 region to those in a region separated by bilayer hBN. The doping, electric field, and temperature dependence of the narrow IX lines are similar for both regions, but their excitonic g-factors have opposite signs, indicating that the origin of narrow IX PL is not the moiré potential.