If you think it's sophistry you're missing the point. Let's break it down:
1. Browsers are open ended tools
2. A knowledgeable user can accomplish all sorts of things with a browser
3. Most people can do very impactful things on browsers, like transferring money, buying expensive products, etc.
4. The problem of older people falling for scams and being tricked into taking self-harming actions in browsers is ancient; anyone who was family tech support in the 2000's remembers removing 15+ "helpful toolbars" and likely some scams/fraud that older relatives fell for
5. Claude is a tool that can use a browser
6. Claude is very likely susceptible to both old and new forms of scams / abuse, either the same ones that some people fall for or novel ones based on the tech
7. Anyone who is set up to take impactful actions in their browser (transferring money, buying expensive things) should already by vigilant about who they allow to use their browser with all of their personal context
8. It is reasonable to draw a parallel between tools like Claude and parents, in the sense that neither should be trusted with high-stakes browsing
9. It is also reasonable to take the same precautions -- allow them to use private browsing modes, make sure they don't have admin rights on your desktop, etc.
The fact that one "agent" is code and the other is human is totally immaterial. Allowing any agent to use your personal browsing context is dangerous and precautions should be taken. This shouldn't be surprising. It's certainly not new.