Nothing I've read specifically mentions the "friends of friends" aspect. It seems that people need to be on YOUR friends list to interact with them. Parents can control who gets added to the friends list by requiring their approval of an addition. Here are various sites that address the settings to accomplish this and other safety measures for children on Xbox Live:
Watch this informative video to learn more about ESRB Ratings, Safety, Family Settings, Online Safety and Kinect Safety Features.
If you allow or enable a minor to use your Service account or an associated account, then:
* You represent that you are the parent or legal guardian of each such minor;
* You acknowledge that you are aware that some features of the Service, and some content available through the Service may contain or expose users to material that is unsuitable for minors, and you agree to supervise usage by minors whom you permit to use the Service. The Service is not intended for use by children under 13, except together with a parent or other adult supervision;
* You acknowledge that we offer “Family Settings” on the Service and the Xbox 360 console, and also offer “Parental Controls” for Windows Vista and Windows 7, that are intended to help you limit access to material that may be unsuitable for minors. By applying Family Settings to an associated account at sign-up, you may, among other things, help to prevent any user of an associated account from making additional purchases and from having access to voice and video chat, which is intended to diminish the ability of such user to communicate with other users. You may view or revise your Family Settings in the “My Xbox” area of your Xbox 360 console, or by logging into your account on www.xbox.com.
Additional information about Family Settings is available at www.xbox.com;
* You are responsible for any material to which a user of your subscription either gains or is denied access (including as a result of your use or non-use of Family Settings or Parental Controls). You acknowledge that use of Family Settings, Parental Controls, or both, is not a substitute for your personal supervision of your minor children or minors for whom you are the legal guardian.
Manage and view Xbox LIVE Online Safety settings
1. Sign into your Xbox LIVE account.
2. Go to My Xbox, and then select your avatar.
3. Go to Online Safety, and then select Change Settings.
If a child account that you own is not stored locally, you can also manage a child account remotely using Family Settings or Family Center.
Xbox LIVE controls come into play only when you take Xbox 360 online, and they're linked to a child's profile and gamertag. When an Xbox LIVE account is created, the service asks for the member's age to determine whether to apply online safety to that account.
Parents are also required to create or use an existing Windows Live ID. The Windows Live ID is associated with the child's Xbox LIVE account and protects the settings from being changed later by the child.
To change a child's settings, first select the child's account name and connect to Xbox LIVE. Once signed in, enter your Windows Live ID password to unlock the settings. To allow or block the child's access to Xbox LIVE, go to My Xbox, Family Settings, Xbox LIVE Access.
Online safety contains many controls, including:
Voice and text: Choose who can communicate with your child (everyone, friends, or no one) on Xbox LIVE. No matter what the setting, your child will still be able to receive new friend requests for you to approve or block.
Privacy: You have the power to approve your child's online friends. Let your child communicate with anybody or only with their friends, decide who can see your child's personalized profile, control who sees your child's online or offline status, and more.
Your child's name, location, and bio are visible to anyone you allow to view your child's profile.
Video status: Choose who can see the videos your child watches in his or her profile.
Explicit music: Choose whether your child can play music and music videos with explicit content.
Friend's List Sharing
Friend's List Sharing is another element of Xbox that you should be aware of. This is a way for your child to interact with their friends and the list can be viewed by other people who are online. You can change these settings so only friends can view the list or you can block it altogether. You can also change the settings to control who your child associates with online. Before a person is added to their friend's list you can set the controls so the request has to be approved by you.
How to Configure / Verify Microsoft’s Xbox Live’s Family Settings to Protect Your Children: