For flares to be generated, stars have to have a sufficiently deep outer convection zone (F5 and later), strong large-scale magnetic fields (Ap/Bp-type stars) or strong, radiatively driven winds (B5 and earlier). Normal A-type stars possess none of these and therefore should not flare. Nevertheless, flares have previously been detected in the Kepler light curves of 33 A-type stars and interpreted to be intrinsic to the stars. Here, we present new and detailed analyses of these 33 stars, imposing very strict criteria for the flare detection. We confirm the presence of flare-like features in 27 of the 33 A-type stars. A study of the pixel data and the surrounding field of view reveals that 14 of these 27 flaring objects have overlapping neighbouring stars and five stars show clear contamination in the pixel data. We have obtained high-resolution spectra for 2/3 of the entire sample and confirm that our targets are indeed A-type stars. Detailed analyses revealed that 11 out of 19 stars with multiple epochs of observations are spectroscopic binaries. Furthermore, and contrary to previous studies, we find that the flares can originate from a cooler, unresolved companion. We note the presence of Hα emission in eight stars. Whether this emission is circumstellar or magnetic in origin is unknown. In summary, we find possible alternative explanations for the observed flares for at least 19 of the 33 A-type stars, but find no truly convincing target to support the hypothesis of flaring A-type stars.