Drupal with "Content Access" is able to achieve the permission control on a page with particular users. To do this, the following steps are required.

1. Go to the particular page that "per-page" access control has been enabled for the content type.
2. Click on "Access Control" from the tab menu
3. Scroll down to the block "Grant access control list" to add the user names to the corresponding "Grant view access", "Grant update access", or "Grant delete access".
4. Visit the user page and click "User permissions" in tab menu. Enable"view devel_node_access information" and save.
5. A hidden role of "_user_role_<uid>_" is created.
6. Visit "Admin" -> "Site configuration" -> "By module" -> "Filter"/"Input format" to add the hidden role to the configuration of the corresponding input filter.

Please note that item #4, #5, and #6 shouldn't be necessary. However, there seems to be a bug or conflict between Content Access modules with other modules so we have to do those steps to get around the bugs.