Either I'm misunderstanding you, or you misunderstood me.

The /Application folder itself is owned by root:

    achilles /$ ls -ld Applications/
    drwxrwxr-x+ 55 root  admin  1870 Jul 20 06:54 Applications/

But that wasn't what I meant. I meant /Applications/Postgres.app. That is owned by the user who installs it to /Applications. Here it is on my machine, for example:

    achilles /$ ls -ld Applications/Postgres.app/
    drwxr-xr-x@ 3 achilles  staff  102 Jul 18 20:17 Applications/Postgres.app/ 

Beyond that, you can login (with no password), this way:

    achilles /$ /Applications/Postgres.app/Contents/MacOS/bin/psql 
    psql (9.1.4)
    Type "help" for help.

    achilles=#

I'm sure it works because I just did it. The setup is arguably insecure, but again I don't think it's meant to be a production database. It's meant, as I understand it, for a single developer to use while coding.