Today I learned it is possible to sign a form and request OpenAI not to store your API calls.

By design, all consumer-grade products created by OpenAI may use your prompts as material to further enhanced their models. That’s the reason why it’s strongly advised not to disclose any personal information when using ChatGPT, for instance.

Their API is subject to a different policy. As stated in their FAQ,

OpenAI will not use data submitted by customers via our API to train or improve our models, unless you explicitly decide to share your data with us for this purpose.

You have to fill in a form to opt in, so there’s no danger of it happening accidentally.

But despite their API usage being a bit safer in terms of privacy, they still keep your prompts and outputs for 30 days to prevent abuse, according to them. If you want your data not to be stored for that period, you’ll have to fill in the opt out form in the same page.