That was my imprecise summary of what the contracts say. The actual language is:
"OpenAI will only use Customer Content as necessary to provide Customer with the Services, comply with applicable law, enforce the OpenAI Policies, and prevent abuse. OpenAI will not use Customer Content to develop or improve the Services, unless Customer explicitly agrees to such use."
"Anthropic agrees that Customer (a) retains all rights to its Inputs, and (b) owns its Outputs. Anthropic disclaims any rights it receives to the Customer Content under these Terms. Subject to Customer’s compliance with these Terms, Anthropic hereby assigns to Customer its right, title and interest (if any) in and to Outputs. Anthropic may not train models on Customer Content from Services."
"OpenAI will only use Customer Content as necessary to provide Customer with the Services, comply with applicable law, enforce the OpenAI Policies, and prevent abuse. OpenAI will not use Customer Content to develop or improve the Services, unless Customer explicitly agrees to such use."
"Anthropic agrees that Customer (a) retains all rights to its Inputs, and (b) owns its Outputs. Anthropic disclaims any rights it receives to the Customer Content under these Terms. Subject to Customer’s compliance with these Terms, Anthropic hereby assigns to Customer its right, title and interest (if any) in and to Outputs. Anthropic may not train models on Customer Content from Services."