This is so code outside the class can use these enumerations as well. Which is likely necessary/useful in some of this class's member functions.
If, for example, ConfigPeer has a function like SetFilter and takes a value of type PEER_FILTER -- in order for code outside the class to reasonably be able to make use of that function, the enum would need to be made public.
IE: outside code could do ConfigPeer::PEER_FILTER filter = ConfigPeer::AllPeers;. This can not be done if those enums are not public.