Humans are able to recognize objects based on both local texture cues and the configuration of object parts, yet contemporary vision models primarily harvest local texture cues, yielding brittle, non-compositional features. Work on shape-vs-texture bias has pitted shape and texture representations in opposition, measuring shape relative to texture, ignoring the possibility that models (and humans) can simultaneously rely on both types of cues, and obscuring the absolute quality of both types of representation. We therefore recast shape evaluation as a matter of absolute configural competence, operationalized by the Configural Shape Score (CSS), which (i) measures the ability to recognize both images in Object-Anagram pairs that preserve local texture while permuting global part arrangement to depict different object categories. Across 86 convolutional, transformer, and hybrid models, CSS (ii) uncovers a broad spectrum of configural sensitivity with fully self-supervised and language-aligned transformers -- exemplified by DINOv2, SigLIP2 and EVA-CLIP -- occupying the top end of the CSS spectrum. Mechanistic probes reveal that (iii) high-CSS networks depend on long-range interactions: radius-controlled attention masks abolish performance showing a distinctive U-shaped integration profile, and representational-similarity analyses expose a mid-depth transition from local to global coding. A BagNet control remains at chance (iv), ruling out "border-hacking" strategies. Finally, (v) we show that configural shape score also predicts other shape-dependent evals. Overall, we propose that the path toward truly robust, generalizable, and human-like vision systems may not lie in forcing an artificial choice between shape and texture, but rather in architectural and learning frameworks that seamlessly integrate both local-texture and global configural shape.