Foreign Marriage Divorce

Legal Marriage in foreign country?
If an American (male) marries a German citizen in Germany and moves to the states, is it a legal marriage in the eyes of USA law. I would assume so seeing how Mexican divorces are recognized.
A friend of mine married a German lady in Germany but never let the US know he married there. He married an American lady now but never got a divorce in Germany.
I am not sure if it is actually a recognized marriage over here if the authorities don’t have any paper work. He had no problems getting married here.
Personally I think he is wrong for doing so but that is just me.