Lythgoe says in an interview posted on People magazine's Web site: "You do not take somebody in that room that you believe is a danger to herself or a danger to Paula. That would not enter our heads."
Goodspeed was found dead of an apparent suicide in a car near Abdul's Los Angeles home last month.
Lythgoe says he remembers Goodspeed as "a lovely girl" and "a great fan of Paula."
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