来自所有主机的 MySQL root 访问权限

我已经在远程Ubuntu机器上安装了MySQL服务器.mysql.user表中对root用户的定义如下:

mysql> SELECT host, user, password FROM user WHERE user = 'root';
+------------------+------+-------------------------------------------+
| host             | user | password                                  |
+------------------+------+-------------------------------------------+
| localhost        | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx |
| ip-10-48-110-188 | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx |
| 127.0.0.1        | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx |
| ::1              | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx |
+------------------+------+-------------------------------------------+

我可以使用标准mysql客户端从同一远程机器命令行界面与用户root进行访问.现在我想添加allow root access from every host on the internet行，所以我try 添加以下行(除了host列之外，它与上一次转储的第一行完全相同):

mysql> SELECT host, user, password FROM user WHERE host = '%';
+------------------+------+-------------------------------------------+
| host             | user | password                                  |
+------------------+------+-------------------------------------------+
| %                | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx |
+------------------+------+-------------------------------------------+

但我个人电脑上的客户继续告诉我(我屏蔽了服务器IP):

SQL错误(2003):无法连接到'46上的MySQL服务器.x、 x.x'(10061)

我不知道这是身份验证错误还是网络错误.在服务器防火墙上，我为0.0.0.0/0启用了端口3306/TCP，这对我来说没关系...