OpenAI's o3-preview reasoning model exceeded human accuracy on the ARC-AGI-1 benchmark, but does that mean state-of-the-art models recognize and reason with the abstractions the benchmark was designed to test? Here we investigate abstraction abilities of AI models using the closely related but simpler ConceptARC benchmark. Our evaluations vary input modality (textual vs. visual), use of external Python tools, and reasoning effort. Beyond output accuracy, we evaluate the natural-language rules that models generate to explain their solutions, enabling us to assess whether models recognize the abstractions that ConceptARC was designed to elicit. We show that the best models' rules are frequently based on surface-level ``shortcuts,'' capturing intended abstractions considerably less often than humans. In the visual modality, AI models' output accuracy drops sharply; however, our rule-level analysis reveals that a substantial share of their rules capture the intended abstractions, even as the models struggle to apply these concepts to generate correct solutions. In short, we show that using accuracy alone to evaluate abstract reasoning can substantially overestimate AI capabilities in textual modalities and underestimate it in visual modalities. Our results offer a more faithful picture of AI models' abstract reasoning abilities and a more principled way to track progress toward human-like, abstraction-centered intelligence.