This is a very rare scenario that one of your network user not able to sync emails through iPhone. Don't worry I already found the answer for you, save your 10-15 minutes surfing the Internet.
Here's an example. The user was able to authenticate when you add the information (e.g. email address, server name, domain, username and password) to the iPhone Exchange Server configuration, but when you check the mail you only see the Inbox and nothing else. This is a permission issue.
Here's how to correct this issue (2010, Technet Microsoft). You need to check the inheritance for the user account.
- Open Active Directory Users and Computers.
- On the menu at the top of the console, click View > Advance Features.
- Locate and right-click the mailbox user account, then click Properties.
- Click the Security tab.
- Click Advanced.
- Make sure that the check box for "Include inheritable permission from this object's parent" is checked.
If the user is a member of certain protected groups such as Domain Administrator, it is normal for this box to unchecked.
2010, Microsoft Technet. http://technet.microsoft.com/en-gb/library/dd439375(EXCHG.80).aspx