MySQL has some special features when making a connection from a remote client that if we do not know can complicate access to a MySQL database from a different machine that hosts the database.
With other databases such as Oracle or SQL Server, once that no firewall or anything like that prevents us from the client machine access to the server, using normally data acces from a database user we can 'enter'.
With MySQL, although access to the port, usually 3306, is open, the database can be configured to shut out external connections, and the result is the same as if the port was closed by a firewall:
telnet mysql.dataprix.es 3306
telnet: connect to address 220.127.116.11: Connection refused
telnet: Unable to connect to remote host
If you get this result should consult the file /etc/my.cnf, and checking for bind-address variable or skip-networking.
If skip-networking is and is not discussed, edit the file and delete it, or make a comment to have no effect and allow external connections: