Are all people "children of God"? Not according to John

I have always found this Scripture interesting.  There are many who say we are all children of God.  In a general sense I suppose that is true.  But in the specific sense that we are entitled to the promises of God as heirs in Christ I believe that is not true.  I point to this Scripture as proof of that belief.

John 1:10-13(NKJV)

He was in the world, and the world was made through Him, and the world did not know Him. 

He came to His own, and His own did not receive Him. 

But as many as received Him, to them He gave the right to become children of God, to those who believe in His name: 

who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

Here is says very clearly that only those who believe in Jesus are entitled to be in the "family of God", heirs with Jesus, entitled to receive God's promises. 

Some would ask, isn't that exclusionary?  Not at all?  Each person gets to decide whether they want to be children of God.  Not a single person is being excluded.  Those who aren't children of God made that decision not to join the family so to speak.  Make sense?