Make sure you add the agent software owner to the OS groups that own the Oracle homes of the monitored databases and their Oracle inventory files/directories. The agent needs to access files and directories in Oracle homes and inventory locations of its monitored targets.
In our env,we have same config.
OEM OS user is not oracle.
You need to make sure that oracle and oem owner is in same group, and group has read,execute privilege and write privilege wherever necessary.
For example,if you are planning to take database backup using OEM,then OEM user/group should have write priv on backup directory.