I do think that’s unnecessarily pedantic- I’m referring to the common meaning of the term, not a specific industry term (particularly when we are not discussing insurance/insurance coverage). I can also find references to other industries that would include treatment more broadly. The point is medical care.
In both of these cases, the focus is more that the parents would not consent. The court in each instances appears to have determined that in fact the parents were not able to withhold consent/consent for their child and that the child was not able to consent/withhold consent. There are much more cases about parental lack of capacity to consent for their child, tied in with child brainwashing. The fact that a judge stepped in each time demonstrates how parents may not always consent for their children, and if they children were competent (which they are not due to their parents brainwashing), they would probably be consenting for themselves.
The removal into state custody in your second example raises a whole other set of issues and consent requirements, but basically further demonstrates that the parents were unable to care for their children (in the opinion of the state). I have expertise in foster care consent to medical care, so I will not derail this thread with that topic but am happy to continue in a new thread if you really care.