Typically, the browser or phone OS does enforce a yes-or-no answer, and if you pick "no" the site or app is not allowed to ask again. So the "Would you like notifications" screen doesn't actually use the host program's API to enable notifications, it just brings up the dialog and asks you again.
This often means that there is a "no and stop asking" option. You just have to realize which dialogs are brought up by the application or the host environment, "accept" the application's request, and then deny the actual permissions request.