Yeesh. Lousy judgement? yep. Should be spoken to? yep. Will have trouble convincing parents she cares in the future, thus reducing her efficacy? yep.
Worth firing? Hell no.
In my dad’s experience (30+ years of running a 4-6 employee general store) it was always worth contesting if the employee’s statement indicated they lied to the first-level bureaucrat. He won probably 95% of his unemployment hearings.