Kate Middleton has long been a magnet for unproven rumors: She pressured an art gallery to remove a royal portrait! She split from her husband! She changed her hairstyle to distract from pregnancy rumors! She did not give birth to her daughter!

This year, speculation kicked into overdrive. Ms. Middleton — now Catherine, Princess of Wales — has lain low since Christmas. Kensington Palace said she was recovering from “a planned abdominal surgery” and unlikely to resume royal duties until after Easter. Conspiracy theorists had other, more sinister ideas. The only explanation for the future queen’s long absence, they said, was that she was missing, dying or deceased, and that someone was trying to cover it up.