It was originally just "truth and justice" when the intro debuted on radio. The "American way" bit was added during WWII, then dropped again postwar, and the narration in the later years of the radio series stressed Superman's battle against prejudice and intolerance (which became the prevailing thread in the stories in '46-'47 or so). "The American way" bit was put back when the radio show moved to television at the start of the '50s, probably because the Cold War and the Red Scare were making declarations of patriotism culturally mandatory again, and that solidified it from then on. So it was the addition of "the American way" to the narration that was politically motivated, not its removal.
Cool.
Speaking of the 50s, how must DCU senator McCarthy have reacted in-universe, every time he read about Superman operating globally, or more less Americanly behind the Iron Curtain?
I really should read JSA Golden Age again sometime soon.