Diagrams convey symbolic information in a visual format rather than a linear stream of words, making them especially challenging for AI models to process. While recent evaluations suggest that vision-language models (VLMs) perform well on diagram-related benchmarks, their reliance on knowledge, reasoning, or modality shortcuts raises concerns about whether they genuinely understand and reason over diagrams. To address this gap, we introduce Chimera, a comprehensive test suite comprising 7,500 high-quality diagrams sourced from Wikipedia; each diagram is annotated with its symbolic content represented by semantic triples along with multi-level questions designed to assess four fundamental aspects of diagram comprehension: entity recognition, relation understanding, knowledge grounding, and visual reasoning. We use Chimera to measure the presence of three types of shortcuts in visual question answering: (1) the visual-memorization shortcut, where VLMs rely on memorized visual patterns; (2) the knowledge-recall shortcut, where models leverage memorized factual knowledge instead of interpreting the diagram; and (3) the Clever-Hans shortcut, where models exploit superficial language patterns or priors without true comprehension. We evaluate 15 open-source VLMs from 7 model families on Chimera and find that their seemingly strong performance largely stems from shortcut behaviors: visual-memorization shortcuts have slight impact, knowledge-recall shortcuts play a moderate role, and Clever-Hans shortcuts contribute significantly. These findings expose critical limitations in current VLMs and underscore the need for more robust evaluation protocols that benchmark genuine comprehension of complex visual inputs (e.g., diagrams) rather than question-answering shortcuts.