I agree that internet dangers are sensationalized. Even with parental control features, you really can't *control* what your DC does on the internet unless you only allow access in your presence. Many internet savvy tweens and teens know how to work around the parental controls and school controls anyway (I teach high school, so I know!).
If you are concerned about access to the internet on a device, my advice would be to not allow your DC to own an internet connected phone unless you trust his/her judgement about how to use it independently.