KABUL—The Sept. 11 attacks that triggered the U.S. invasion of Afghanistan also uprooted 16-year-old Abdul Ghattar from his village in war-torn Helmand province, bringing him to a desolate refugee camp on the edge of Kabul.

Yet Mr. Ghattar stared blankly when asked whether he knew about al Qaeda's strike on the U.S., launched a decade ago from Afghan soil.

"Never...