“It was two fighter jets dancing with this thing going around and around it,” said Jeffrey Billie, a retired defense contractor who lives in Pawleys Island, S.C., and witnessed the one-sided confrontation. Mr. Billie said a third jet flew near the balloon and fired a missile just as the craft crossed the coastline. “Then, of course, the round big white ball that we saw all of the sudden looked like a shriveled Kleenex.”