Abstract We now have several observational examples of misaligned broken protoplanetary discs, where the disc inner regions are strongly misaligned with respect to the outer disc. Current models suggest that this disc structure can be generated with an internal misaligned companion (stellar or planetary), but the occurrence rate of these currently unobserved companions remains unknown. Here we explore whether a strong misalignment between the inner and outer disc can be formed without such a companion. We consider a disc that has an existing gap — essentially separating the disc into two regions — and use a flyby to disturb the discs, leading to a misalignment. Despite considering the most optimistic parameters for this scenario, we find maximum misalignments between the inner and outer disc of ∼45○ and that these misalignments are short-lived. We thus conclude that the currently observed misaligned discs must harbour internal, misaligned companions.