Removing an agent from a cooperative team to measure its contribution seems natural, yet in multi-agent LLM systems this evaluation distorts the result it claims to measure. This failure is not isolated: learned critics, trajectory-level baselines, and agent-removal counterfactuals all inherit from standard multi-agent reinforcement learning a premise that exact counterfactual evaluation requires privileged environment access, and therefore approximate. In cooperative LLM systems, this premise is false. Interaction histories are deterministic functions of observable text with no hidden state, so any decision point can be restored exactly, making direct causal measurement possible without parametric approximation. C3 exploits this property by fixing the complete history at each decision point, sampling alternative actions under a frozen behavior policy, and computing unbiased per-decision advantages through a parameter-free leave-one-out baseline. Across six benchmarks spanning math reasoning and code generation, two model families, and two multi-agent topologies, C3 consistently outperforms all baselines; a controlled decomposition confirms gains originate from credit quality, not architecture, while checkpoint restoration reduces training token consumption. The exact solution proves simpler, cheaper, and more effective than all approximate alternatives. The same structural property that enables exact credit also enables exact verification: three independently computable diagnostics, credit fidelity, within-group variance, and inter-agent influence, constitute the first method-agnostic auditing tool for multi-agent LLM credit assignment. Our code is available at https://github.com/EIT-EAST-Lab/C3