How do I change what's returned by /usr/libexec/java_home
The problem here is that Oracle have chnaged the meaning of JRE on Macs.

The Apple and Sun definition is JRE is the runtime for apps and web applets.

Oracle's definition of JRE is for webapps only. This means that it does not change /usr/bin/java

The JDK definition had not changed. Oracle has this at http://www.oracle.com/technetwork/java/javase/downloads/index-jsp-138363.html#javasejdk

Oracle does also have a old style JRE that changes /usr/bin/java but have hidden it