Trivia: Co-stars James Remar and Cary-Hiroyuki Tagawa were both in the "Mortal Kombat" film franchise. Tagawa played the lead villain "Shang Tsung" in 1995's "Mortal Kombat," which came out a year before "The Phantom." And Remar played Lord Raiden, one of the lead heroes, in "Mortal Kombat: Annihilation," which came out one year after "The Phantom" in 1997.
Trivia: The film was originally written as a bit of a comedic spoof of superhero and adventure stories by "Gremlins" director Joe Dante and famed screenwriter Jeffrey Boam. Dante was planning on directing it. However, the movie was paused due to budget concerns, and Dante left the project. When it was put back into production, the script was re-written by several ghost writers, and director Simon Wincer decided to play the comedy 100% straight, which original director Dante felt was a huge mistake.
Trivia: Billy Zane was a fan of the character and took the film very seriously. He spent a year working out and doing weight training to build muscle mass, so he wouldn't have to wear a fake muscle suit. He'd also leave set in full costume and drive around, get lunch, etc.
Answer: She was preoccupied trying to escape from the bad guys and annoyed that a guy in a purple suit, was trying to save her, when she said, "I can do it myself." It was most likely later, in New York, when the met face to face. Kit and Diana, when she put two and two together. Again was too preoccupied trying to save the world to pause and confront him.