In a statement released Wednesday, Joel and Brinkley say their daughter's actions came "while suffering a devastating heartbreak." The statement didn't specify what her actions were.
Joel and Brinkley also say a report published Tuesday in the New York Post was "false." The Post reported the 23-year-old attempted suicide after a fight with her mother during a family vacation.
A spokeswoman for the Post didn't immediately comment.
A publicist for Alexa Ray Joel said this week she was feeling better and was with family.