Using oracle easy connect does it really connect to the remote DB?
The answer is very simple. The ! prefix in sqlplus executes the following text as a command in the local shell. 

In your case it's executing the Unix hostname command locally.

Query v$instance to check the name of the machine you're connected to.

There are ways to execute local Unix commands via the database, but it's seen as a huge security hole, so I won't document them here.

ssh (assuming Unix) into the database host instead.