When they start flying airplanes into our buildings, murdering thousands and telling us they are intent on taking over the world, making Europe a new Caliphate and pushing Israel into the sea, the idea is wrong.
As for this history, yes, that is wrong as well.
In 1801, Madison was appointed Secretary of State by the new president, Jefferson. James Madison as Sec. of State guided the negotiations that resulted in the Louisiana Purchase (1803) and supported American suppression of the Barbary pirates in the Tripolitan(1803-05).
Following the war with Tripoli, the United States ordered its Navy ships in the Mediterranean to return home. Conflict with England was heating up and finally exploded in the War of 1812. By this time, a new dey, Omar, had taken over in Algiers. He ordered the capture of American merchant ships because of overdue U.S. tribute. President Madison responded by getting Congress to authorize military action against Algiers in February 1815. He sent a squadron of nine warships to end Barbary tribute. Reference.
When I say international entanglements, I am talking about the UN, NATO, NAFTA, G8, etc. Avoiding international entanglements in no way means not defending ourselves from foreign aggression.