MySQL uses internet sockets to access the database. That implies that, not only can you access the MySQL server from a script from a different computer over the network, you can even access it over the internet, if MySQL is set up to allow login access for remote users. So it's both a blessing and a curse.
See here on how you (or at least someone with database admin access) can allow remote access. 'localhost' means access from the same machine, while '%' means access from anywhere on the internet who can reach the machine (as a firewall might still block it). I think it must be possible to specify a specific host, or even an intranet mask, like '192.168.%', so remote login access is automatically limited even if the firewall allows access; but I've not ever actually tried it, nor have I read anywhere that it is possible. It just looks like a very database-like behaviour to do it like that.
Update Whoops. At the bottom of the same page that I linked to, it clearly describes that it does indeed work as I suspected. I quote:
To create a user who has access from all machines in a given domain (for example, mydomain.com), you can use the “%” wildcard character in the host part of the account name:
To do the same thing by modifying the grant tables directly, do this:
mysql> CREATE USER 'myname'@'%.mydomain.com' IDENTIFIED BY 'mypass';
mysql> INSERT INTO user (Host,User,Password,...)
mysql> FLUSH PRIVILEGES;