This is correct, "When you activate a Cloud Billing account, all use of Gemini API and Google AI Studio is a "Paid Service" with respect to how Google Uses Your Data, even when using Services that are offered free of charge, such as Google AI Studio and unpaid quota of Gemini API."

There are a few conditions that take precedence over having-billing-enabled and will cause AI Studio to train on your data. This is why I personally use Vertex