Despite the emergence of large language models (LLMs) for visual data storytelling workflows, there are open questions about how authors decide what activities or tasks to entrust to them and what should be "protected" or maintained under human control. To investigate this, we interviewed a cohort of 12 expert visual data storytellers. Our analysis shows that participants rarely treated LLMs as autonomous storytellers. Instead, they tend to selectively delegate execution-oriented tasks to LLMs while retaining control over activities that shape narrative intent and story meaning. Our findings show that LLM assistance is most productive after human seeding and constraint-setting, and that it shifts labor from production to verification. We discuss design implications for boundary-aware authoring tools, data-grounded generation, low-fidelity ideation, and reporting practices for LLM-based visualization research. Supplemental materials for this paper are available at https://osf.io/hcnp6.

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