I just thought of a couple of jazz standards that qualify if we allow instrumentals: St. Thomas (written by Sonny Rollins in 1956) and Watermelon Man (written by Herbie Hancock in 1962). Both have been performed and recorded by many artists.
I wonder if what was meant instead of “The Long and Winding Road” is the song which starts with the words “The road is long, with many a winding . . .”, although the title of that song is actually “He Ain’t Heavy, He’s My Brother”. But, you’re going to object, that’s not American either, since it was made famous by the British group called The Hollies. Yes, but it was written by two Americans and was first recorded by an little-known American singer before it was recorded by The Hollies.