I live in the Bay Area so I don't know for sure if the rules are the same in Kansas but when we go to the Dr.'s, and it is for an injury, the nurse and the Dr. both will ask the child what happened.
My son is high functioning autistic but very non-responsive around strangers. When we went in once for a sprained wrist from falling off the monkey bars at school, every time they asked him what happened he would only look at me. I tried to answer for him and both the nurse and the Dr. silenced me and told he and I he needed to answer. He finally gave a one word answer like, "fell" and practically yelled, "mom, you talk." They begrudgingly let me explain. After the appointment the Dr. pulled me aside and quietly apologized, said she had looked up his records and saw he was autistic and that the were mandated to ask the child what happened.
It has happened a few more times since that first time but now that I know what an injury appointment entails, I prep him on the drive over and he's a little older and a littttle more flexible.
If the Dr.'s would question Lucas about his injuries I doubt EG would have brought him so the note would more than likely be fake.