In terms of theories about accidents, there is almost no accident theory that would create an major issue in taking him to the doctor, EXCEPT if the accident included someone laying hands on him in some fashion. There might suspicion of abuse in some situations but his medical history (or lack of history of unexplained or poorly explained cuts, bruises or breaks) and family support would probably mitigate a claim of abuse. Medical neglect would come into play but usually has more than one instance of not seeking help in an emergency or medical care that involves medications (antibiotics, daily medications).
Falling on hike, falling on a bike, falling playing, etc are fairly routine and would be cause for clarifying questions. but would not (at his age) because for concern unless the injury was atypical like spiral fractures or large bone fractures where the story doesn't add up.
Ingesting substances, known or unknown, would be cause for concern given his age. Is the child experimenting with substances to get high (airplane glue, rubber cement glue, bath salts, or any other fashionable kid culture substance? If yes, going for medical attention would probably result in a referral for counseling. Does the child have an underlying condition that causes them to want to eat or ingest harmful substances? I doubt he had a condition like Pica. If the child was saying they ingested no substance but a tox screen shows differently, the question of lying or others providing comes into play. Eye drop poisoning seems to be making a comeback (I think I know why---b/c it is not looked for generally). But, if someone was poisoning him, that is not accidental.
These kids were supervised with at least one parent who monitored their movement. The idea that an accident would be cause for concern in seeking medical treatment does not make sense to me. There was not an ongoing custody battle that would cause concern of loosing custody either. Now, accidental harm inflicted by an adult, that I see as a real possibility for not seeking medical attention for fear of abuse charges and/or a spouse who would throw you out if they became suspicious.