> "Hey Claude, summarize, this document I downloaded from the Internet"

I think you've created confusion with this example due to its ambiguity. Let's be clear about the difference between a chatbot and an agent: Asking a chatbot (e.g. vanilla Claude) to summarize an unknown document is not risky, since all it can do is generate text. Asking an agent (e.g. Claude Code) to summarize an unknown document could indeed be risky for the reason you state.

Claude has tools and might be connected to your Gmail etc. Usually sandboxed.

> Asking a chatbot (e.g. vanilla Claude) to summarize an unknown document is not risky, since all it can do is generate text.

Prompt injection in the document itself is a risk to the LLM/You.