You (or your hosting service) can configure access permissions on the remote server as desired, but the result must be the only one: scripts should be able to access files for both reading and writing, which means that a primary "user" under which the Apache server runs, must be able to access files with these modes.

At the same time, if a shared hosting is the case, other users must not be able to read or write your files via their scripts. Your "user" should be able to rewrite files via the FTP as well as modify uploaded files from within scripts.

The problem is that each hosting provider has their own security policy and preferences: while some limit access to other's files even with a 777 permissions, some run the Apache web-server under a single user for each virtual host.

Some hosting providers launch the server process under user nobody:group by default. The files that a hosting client stores on a server, should be accessible by the Apache. It means that they has the attribute read for all set, or a user (file owner) and server must belong to the same group. In the latter case, files must be accessible by the group members for reading (FTP servers assign this kind of permission).

This approach hits hard the security because if all users belong to the same group, they can read each other's files. Say, a user opened a page in the browser which runs a CGI script. As the script in fact is executed by the Apache server which runs under nobody, the script will run with permissions assigned to this user.

The Bitrix Site Manager remains fully functional with any access permission that you have specified at the installation time.

To allow the Bitrix Site Manager work correctly with your CHMOD, you have to set the following constants in /bitrix/php_interface/dbconn.php:

define("BX_FILE_PERMISSIONS", 0777); 
define("BX_DIR_PERMISSIONS", 0777);

Substitute 0777 with values allowed by your hosting for files and folders.

The following values are common to most hostings:

0644 - for files,
0755 - for folders.

You can set the access permission level manually by using CHMOD in console.

The following command sets the access permission level for both files and folders:

chmod -R 644 *

You can use the following command to set rights for folders only:

find . -type d -exec chmod 0755 {} ';'

Some FTP clients allows to recursively set rights for files and folders. For example: FlashFXP version 3.xx. FlashFXP allows separate rights for files and folders.

You should consider the following settings: Separately set File and Folder attributes and Apply changes to all subfolders and files. 

Individual access permission levels are applied to these settings:

Folder permissions		File permissions

The Site Explorer displays the file and folder attributes as well as the owner and user group information (for xNIX) in the Access permissions column.