In Discover Oracle Homes we check for the oraInst.loc file which will be in either /etc/oraInst.loc or /var/opt/oracle/oraInst.loc depending on the OS. From here we find the oracle inventory directory which this file points to. We then will traverse that to find the Oracle installations.
The Delphix_OS user will need access to /etc/oraInst.loc or other listed above and the oracle inventory location as well as read access to the files under the inventory location. We need to gather data from some of the oracle xml files to determine the Oracle Home locations etc.
We will then need access to the ORACLE_HOME as well.
The best solution is to run hostchecker on any new target or source server to verify things are setup correctly as the delphix_os user.
I hope this helps.
Cheers,
Dave G.