If you the user ask it to access a page (or do any task that probably needs that access), then it'll try to do so the best it can. Anything less is user-unfriendly behavior.
The whole succeed-at-all-costs idea is a big part of why there have been so many massive security screwups lately.
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?