Actually, a military medic does not receive the training that a paramedic in the civilian sector does. As an instructor, I can tell you that a coworker of mine was a special forces medic (I have seen his DD214- he is not a poser) and he has large gaps in his knowledge base. Similarly, a civilian medic does not have the training in adult trauma that a military medic does- two totally different jobs. With that said:
1 A military medic would not have the pediatric training that civilian medics would.
2 Even with that training, the visible signs and symptoms of a CHI (Closed head injury) are late stage signs, and they will appear after the condition is well advanced.
In addition:
All patients have the right to accept or refuse medical care for themselves. That is called "informed consent," or "expressed consent." In the case of a minor, the parent is the one who gives this sort of consent or refuses care.
There are certain cases where a person loses that right. Included in those times is when the patient is incapable of making an informed decision, cases like a head injury, stroke, intoxication, disease processes such as dementia, or if the patient is under the influence of drugs, alcohol, or other substances, or if the patient is unconscious. In these cases, the law allows the provider to assume that the patient would want to be treated, if they were able to make the decision for themselves. This is called "implied consent."
A court (in some cases, so can cops and medical personnel) can also order medical treatment, and this is called "involuntary consent." (I know, an oxymoron.) In various states, there are laws that allow medical facilities to treat, even over the objections of the patient, guardian, or parent, if the lack of treatment would constitute a danger to the patient, or in this case, the child. Frequently, parents who are abusing their children do not want their children to seek medical care, because they are fearful of being caught. This is also common in cases of elderly abuse.
It is a complicated set of laws, and we spend a lot of time covering it with our students in class. Even then, not being attorneys, it still is not always understood. There have been numerous books and law cases written on this very subject.