I'm not sure why you're asking but my experience is that it is up to each person and each medical provider how they handle the transfer of records and if they even request them at all. I believe someone could easily move and choose not to get a new dr in their new location and/or never request the transfer of records. For example, if Lori moved to Idaho and didn't bother to get a new dr for the kids then their old pediatricians office in AZ would never know she moved at all. It's her responsibility to get them a new dr and she would have to disclose any and all medical conditions to the new dr (every new dr you go to you fill out a bunch of forms asking your medical history). In my experience drs only request past records from other providers if you have an ongoing medical condition and they need the documentation. But that is not always the case and it apparently depends on the medical condition and the dr.
For example, I carry an epipen for a severe allergy. Some drs want to know the name of the dr who first diagnosed my allergy so they can request official record of diagnosis before they will prescribe me a new epipen prescription (I had bloodwork that proved my allergy was severe). Other drs will prescribe me an epipen prescription renewal without asking for the dr's name or any evidence of my diagnosis. Most drs take me at my word when I say I have an allergy and show them my current epipen I carry, which I appreciate as it's a life threatening situation if my epipen expires and I can't get a new one OR if the new dr doesn't note an allergy and I'm later prescribed something I'm allergic to.
Bottom line is there doesn't seem to be any uniformity in our laws on when drs are supposed to request medical history records. It would be easy to "forget" to disclose something and the new office wouldn't think there was any need to request records. Or it would be easy to move somewhere and not bother to find a new dr at all. Now that said, most insurance plans these days require at least a yearly physical (or give incentives for you to get one) and schools usually require kids to be up on their immunizations (exceptions being for health or religious reasons on a state by state basis).
If Lori took the kids to a new pediatrician in Idaho she could have presented their immunization records for school admission only and say the kids have no underlying medical conditions at all. The new dr might not request any records from their former dr in that case. She could have omitted JJ's past diagnosis of autism and it might not have been found out in Idaho. We already know that JJ's school records were never transferred from AZ. With him having autism he likely would have had an IEP:
Individualized Education Program - Wikipedia
IMOO, that IEP should have been requested by the new school if they were made aware he had autism. I strongly suspect that Lori didn't tell the new school JJ's diagnoses or perhaps she told them something else that prevented the new school from trying to request his records? I'm not sure what she could have told them. It seems like she never informed the old school of JJ's new location either so the old school had no place to send his records. Lori has moved states many times in her life so if she failed to take the right actions to get records transferred (either medical or school records) it was done on purpose.
MOO.