Last week, K-pop supergroup Girls' Generation got an unprecedented U.S. television showcase on "Live! With Kelly," the Reegeless morning show currently featuring Kelly Ripa and a revolving-door series of daily guest hosts. For those who caught it, the segment offered up one of television's rare magic moments — not during the musical performance itself, but in the brief interview immediately afterwards.

The Girls had just pulled off a crowd-pumping rendition of their first U.S. single, "The Boys," complete with their signature...