No. World War II is a perfect example of why that old saying is false. Americans were all loving the Communists during the war because Communists were helping us fight the Fascists. Russia was our numero uno. But after the war our "enemy of our enemy" became our scariest enemy. Early Germany was the same way. Otto von Bismarck had Prussia ally with the Austrians to beat a common enemy, the Danes. After a combined Germanic assault defeated the Danes he then turned on Austria and beat the tar out of them. History shows that an enemy of an enemy can be an ally but don't dare think of them as a friend.
