Luminescence can indeed be measured using standard multiwell plate readers, as supported by assay protocols and biosensor applications designed specifically for plate-based detection equipment.
The claim states that luminescence can be measured using a fluorescence plate reader (or more broadly, a multiwell plate reader capable of luminescence detection). Multiple papers discuss utilizing plate readers for luminescence assays or combining fluorescence and luminescence readouts in microplate formats (e.g., papers 7 and 8). The evidence clearly supports the validity of performing luminescence measurements on plate reader platforms.