According to your post...you lied about what the father said. The father said he did not have "unsupervised access to them". That is NOT the same a no access. It was not a crime for the father to purchase the gun...it is not a crime to gift that gun to his son...it is not a crime for the son to possess the gun.
If the legal authorities who investigated the kid did not find probable cause to continue the investigation or to take any action related to the threat, the neither the father nor the kid should lose their constitutional right.