This question was posted in response to the following article: http://help.adobe.com/en_US/ColdFusion/10.0/Developing/WSc3ff6d0ea77859461172e0811cbec22c2 4-7406.html
The comment "you can also connect to any mailbox whose owner has delegated access rights to the login user name" is too generic and doesn't provide the level of detail needed. I understood that to mean that if the owner delegates just calendar access rights to my user account that I can query their calendar. However this doesn't appear to be the case. The user had to delegate both calendar access and inbox access to my user account before I was able query just their calendar events.
The other way I found to accomplish this is by creating an Exchange account with Exchange Administrator privileges and granting it access to the users mailboxes. I would then use this Exchange account for the username and password in the cfexchangeconnection and could query the events of any users that the Exchange account had access to.