How to disable SET PASSWORD for users?

How to forbid the user changing his password?

According to the official doc, SET PASSWORD works only for users having UPDATE priviledge on the mysql.user-Table:
http://dev.mysql.com/doc/refman/5.1/de/set-password.html

However, any newly created user with no privileges at all can change his password with

SET PASSWORD = PASSWORD('verysecret');

PHP:

How can I deny users changing their passwords?

 

It is true when the use want to change password for other users.

 

Do I understand this right: There is no way to prevent users from changing their own password in MySQL?

 

Yes, AFAIK.