This claim is true but it also depends on the children's overall well-being. The article mentions that Red 40 dye contains chemicals that come from petroleum that can be harmful for the body. The article also mentions that there are also certain qualities in children that can make dyes more harmful, for example: ADHD, anxiety, and Oppositional defiant disorder. Having experienced the harm of Red 40 or food dye in general, I can say that I do notice a difference in the way it affects my behavioral and mental well-being.
Although, nothing has been proven, the article mentions that there is research showing that food dyes can contribute to the hyper-activity of children. The National Library of Medicine has also done research on this topic, specifically with children that have ADHD and have found a relationship between behavioral effects and artificial food dye. The article linked has valuable information that can help support this claim.
https://pmc.ncbi.nlm.nih.gov/articles/PMC3441937/