Laura Rhodes, 13, from Neath, took a drug overdose and died last September.
Her best friend took an identical number of pills but survived.
Michael and Yvonne Rhodes insist their daughter's death was triggered by bullying at Cefn Saeson comprehensive in Cimla, Neath, an allegation the school has strongly denied.
A two-day inquest in Neath last month heard that Laura was taunted over her weight and sexuality while at the comprehensive, which she had left a year before taking her life.
But child psychiatrist Dr John Talbot, who compiled a report on the two girls, told the inquest the school was not to blame.
The motives for the suicide pact had been the girls' fear of separation from each other, anxieties about homophobia and punishment.
Neath Port Talbot council and Cefn Saeson again expressed sympathy to Laura's family, but said they were satisfied with the coroner's finding that name-calling was not the cause of her death.