Humans are susceptible to optical illusions, which serve as valuable tools for investigating sensory and cognitive processes. Inspired by human vision studies, research has begun exploring whether machines, such as large vision language models (LVLMs), exhibit similar susceptibilities to visual illusions. However, studies often have used non-abstract images and have not distinguished actual and apparent features, leading to ambiguous assessments of machine cognition. To address these limitations, we introduce a visual question answering (VQA) dataset, categorized into genuine and fake illusions, along with corresponding control images. Genuine illusions present discrepancies between actual and apparent features, whereas fake illusions have the same actual and apparent features even though they look illusory due to the similar geometric configuration. We evaluate the performance of LVLMs for genuine and fake illusion VQA tasks and investigate whether the models discern actual and apparent features. Our findings indicate that although LVLMs may appear to recognize illusions by correctly answering questions about both feature types, they predict the same answers for both Genuine Illusion and Fake Illusion VQA questions. This suggests that their responses might be based on prior knowledge of illusions rather than genuine visual understanding. The dataset is available at https://github.com/ynklab/FILM