A patient, sitting quietly in a clinic waiting room, suddenly and involuntarily perceives a detailed scene unfolding in front of him as though it were happening right now, with no awareness that he is remembering rather than currently perceiving something. Before revealing the answer: is this eidetic imagery?

No, this is more consistent with a visual hallucination (or possibly a flashback, depending on further detail) than with eidetic imagery. Eidetic imagery specifically requires the patient to recognise the experience as a memory of something previously seen; here, there is no such recognition, and the scene is instead perceived as though currently happening, involuntarily intruding on his awareness. This absence of recognised, voluntary memory recall, and the sense of the scene unfolding in the present, points away from eidetic imagery.