Well the “private” account features on facebook are not really private. Here is the issue...if you access any of the 3rd party “games”, “apps” they have access to some of your account information even if it is marked “private” and quite frankly you know NOTHING about the app developers and what they are doing with your facebook info...that you think is private.
Also keep in mind if they link your profile to other “non-private” profiles and those profiles have “bad” things in them...well as they say...the crowd you keep...
To be honest I know nothing about facebook.All my kids and most of the older grandkids are on it.I just know that they all have private accounts and nice pages.But your right you have to be careful.