Let us break this question down into a few parts.
1) Is constant exposure to "scary" events dangerous?
There is a growing body of evidence that today’s constant flow of media messages can produce fear and anxiety in children. Constantly viewing frightening and sensational images can change a child’s view of the world and affect their sense of well-being. Limited exposure may only cause a child to feel scared or upset temporarily, however, more intense exposure may cause a child to experience long-lasting fear or anxiety that may continue into adulthood.
Therefore, it is safe to conclude that constantly hearing about violence as well as fantasy imagery and themes (such as magic, villains and heroes) can frighten and confuse children and, in some cases, introduce fears that can last into adulthood.
2) Does the above apply to our children?
Fortunately, most of our children are not exposed to violence on a constant basis and are even somewhat sheltered from the regular grueseome news of bombings, killings, and terrorism that adults may be exposed to (at least the imagery part).
In addition, going to the other extreme of totally sheltering our children is not either recommended.
A child who has a relatively happy childhood and regularly exposed to positivity should be able to tolerate gradual exposure to the realities in life at an appropriate pace. Thus for the majority of our children, limited exposure to things like holocaust stories and scary color war breakouts during the upper elementary grades is recommended, in a general sense.
3) So, are camps over exposing children and causing damage?
It is not clear if the camps you are referring to are doing what has always been done--limited exposure--or something more on a quantitative or qualitative level. If multiple children are experiencing negative reactions, it is recommended that camp staff speak with a competent child anxiety & trauma specialist to reassess.
A final point for parents (and camp staff) is the importance of keeping the individual child in mind. Some children, based on their individual temperament, may be particularly sensitive to these things. Others may have experienced their own trauma and are unable to handle it. Parents should be aware of their child's challenges and, where necessary, a child should be removed from a particular activity.