The issue here is whether the harness is doing it. Claude Code is doing it. Codex is not.
Seems that way... Here's how I interpreted it:
> claude code divulged my email to arbitrary 3rd parties in the User-Agent request header while conducting web searches without my permission
"Claude Code" refers to the harness, not the model. Web search is also one of the tools provided to the model by the harness.
https://code.claude.com/docs/en/tools-reference#websearch-to...
https://platform.claude.com/docs/en/agents-and-tools/tool-us...