You need internet access if your app itself needs to access the internet, but opening a url means your browser will do that, you simply ask the browser to be opened.
Activities that can be safely invoked from a browser must support this category. For example, if the user is viewing a web page or an e-mail and clicks on a link in the text, the Intent generated to execute that link will require the BROWSABLE category, so that only activities supporting this category will be considered as possible actions. By supporting this category, you are promising that there is nothing damaging (without user intervention) that can happen by invoking any matching Intent.
As I stated in the question, I want to open the browser, and that’s all. I don’t want to open it within the application; I’m just calling the user’s browser. See my answer for the solution.