I think this is the correct way of phrasing it. "Suggestions based on X" merely implies that information on X is now sent to an (additional) 3rd party, and does

I think this is the correct way of phrasing it. "Suggestions based on X" merely implies that information on X is now sent to an (additional) 3rd party, and doesn't state so explicitly. In fact I would say the lack of explicit statements on what data is sent is a deliberate attempt to hide that fact from users. Note how similar the language is to the privacy options on Google's Android.