Well if you disable web search, that's just making that built-in tool unavailable to the agent (when it's enabled, the agent gets usage info and guidance about it in its context). Given a task in which online resources may be useful, the only thing the agent knows is that it could search the web, and that there are a variety of means (curl, wget, urllib in python, etc) which may be at its disposal. Without you telling it specifically not to search the web (or that guidance coming from elsewhere) or blocking internet access, there's no reason it wouldn't use that avenue in fulfilling its task.
I am well aware of why this phenomenon happens. That does not mean that I think that OpenAI’s (and Anthropic, etc’s) training or harness behavior is appropriate.
Would it really have been so hard to encode an indication of whether use of the public Internet is permissible in the prompt and to train the models to not attempt to exceed authorized access?
I'd say for the greater majority of users, when they tell their agent to do some task, particularly any that involves research (which isn't specifically about something on the local machine), using the internet is implicitly expected. Imagine having to go into my computer settings to flip an "allow internet usage" each time I want to use a browser. That's extremely user-unfriendly, and there's 0 reason to encode a default internet block when users expect their agent to handle their given tasks with minimal friction (I still recall the frustration of babysitting Claude permissions just a few months ago; auto-mode was the best feature ever for those of us who didn't want to go YOLO).