What are the default settings for accessing MySQL remotely?
You will have to resort to removing remote access from the MySQL users themselves.
To find out who has remote access, run this
SELECT user,host from mysql.user
WHERE host NOT IN ('localhost','127.0.0.1');

This will show you everyone that can login to MySQL from specific access points as well as broader network specifications.
You could run the utility mysql_secure_installation which do the following:

You can set a password for root accounts.
You can remove root accounts that are accessible from outside the local host.
You can remove anonymous-user accounts.
You can remove the test database (which by default can be accessed by all users, even anonymous users), and privileges that permit anyone to access databases with names that start with test_. (I posted a question and answer about this weird aspect).

UPDATE 2013-07-02 13:11 EDT
I see you have skip-networking in the my.cnf and you removed bind-address=127.0.0.1. I don't think the two options belong together. Why?
The option skip-networking disables TCP/IP. Using 127.0.0.1 as a bind-address implies TCP/IP. The two can never really mix. They are meant to be mutually exclusive. Use one or the other, not both at the same time. This makes sense because when you read the MySQL Documentation for skip-networking and bind-address, one does not mention the other.