Vision-language navigation requires agents to reason and act under constraints of embodiment. While vision-language models (VLMs) demonstrate strong generalization, current benchmarks provide limited understanding of how embodiment -- i.e., the choice of physical platform, sensor configuration, and modality alignment -- influences perception, reasoning, and control. We introduce Embodied4C, a closed-loop benchmark designed as a Turing test for embodied reasoning. The benchmark evaluates the core embodied capabilities of VLMs across three heterogeneous embodiments -- autonomous vehicles, aerial drones, and robotic manipulators -- through approximately 1.1K one-shot reasoning questions and 58 goal-directed navigation tasks. These tasks jointly assess four foundational dimensions: semantic, spatial, temporal, and physical reasoning. Each embodiment presents dynamic sensor configurations and environment variations to probe generalization beyond platform-specific adaptation. To prevent embodiment overfitting, Embodied4C integrates domain-far queries targeting abstract and cross-context reasoning. Comprehensive evaluation across ten state-of-the-art VLMs and four embodied control baselines shows that cross-modal alignment and instruction tuning matter more than scale, while spatial and temporal reasoning remains the primary bottleneck for reliable embodied competence.