MySQL won't recognize ALTER on timestamp

Question

I have a MySQL oddity I haven't seen before and could use some help.

I have a users table that was created (not by me) with these two fields:

`date_entered` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
`date_modified` timestamp NOT NULL DEFAULT '0000-00-00 00:00:00',

These are the only 2 timestamp in the table.

However, that's incorrect so I ran this update statement:

ALTER TABLE `users` 
  CHANGE `date_entered` `date_entered` TIMESTAMP NOT NULL,
  CHANGE `date_modified` `date_modified` TIMESTAMP NOT NULL;

This works fine on my localhost (Wampserver MySQL 5.6.17) but does not work on my production machine (Windows MySQL 5.6.16) and keeps defaulting back to having the DEFAULT set for both fields.

Is there something I need to configure in MySQL or somewhere else to get rid of these defaults? I'd like to remove both but especially the ON UPDATE CURRENT_TIMESTAMP since it makes the data wrong.

Thanks!