Here, courtesy of my excellent email and web hosting provider http://www.luxsci.com, is the reason why this irritating issue, about which I have tweeted in the past, happens.
This may happen if you setup an IMAP account on your iPhone and check your folder list before you set the IMAP Path Prefix to “mail” in the Advanced Settings. It may also happen if you originally set the IMAP Path Prefix incorrectly in the Advanced Settings. The correct IMAP Path Prefix is “mail” without the quotes. Your “Inbox” may still be grayed [sic] out even after changing the Path Prefix to the correct path. This is because the iPhone creates an additional “Inbox” folder when it does not find one, and this extra “Inbox” in your folders can cause the iPhone to get confused. To resolve this, contact support and have them delete or rename the extra “Inbox”. This should resolve the problem.