Plot hole: "Dorothy Michaels" does not exist, but suddenly becomes famous. It is simply not feasible that nobody looks into her background! Not one single print or television reporter is interested in her life story? Nobody has ever wondered where she came from, has checked into what other roles she had played, or has expressed interest in her personal life? That's impossible.
Plot hole: Since "Dorothy Michaels" does not exist, she will not have a Social Security number. Even with her agent acting as a go-between, the television production company, her employers, would have to have this for their records. Supplying a false Social Security number is a very serious offense (and is instantly detectable), as is employing someone without one.
Answer: What she said was a fantasy - big difference between saying that in conversation and actually having it said to her.
Thank you.