Spreadsheet agents are converging on elaborate multi-agent designs, yet it is unclear how much of their performance comes from the agents rather than from the action interface they share. We answer this with SheetMind, a Manager-Action-Reflection framework, in a controlled study over all 221 tasks of the SheetCopilot Benchmark: five architectural variants, four backbones, exact McNemar tests on paired outcomes, and a checker reproducing the official chart and pivot comparisons. Replacing the high-level action API with primitive cell operations costs 47.1 points (p < 0.0001) and leaves the agent below a do-nothing baseline, whereas both extra agents together are worth 3.2 points: the Reflection Agent adds +4.5 (p = 0.013), the Manager +1.4 (p = 0.68). Decomposition instead changes how the system fails, cutting silently wrong outputs from 33% to 25% of tasks (p = 0.010). Capability saturates: GPT-5 and the five-times-cheaper GPT-5-mini are not significantly different (61.1% vs. 58.4%, p = 0.15), while GPT-3.5 loses 16.3 points and fails differently. A reflector must judge the step it just took, not the subtask. SheetMind reaches 61.1% Pass@1 with GPT-5 on the full SCB-221, against a do-nothing baseline of 9.0%. Accuracy comes from the operations an agent can name; the agents decide how it fails.

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