This is what I found, while trying desparately:
Instead of clicking on the iCal attachment in the mail message, dragging the attachment on the Month View puts the invitation on the right day, with the right (intended) attendees.
I still would like to learn what initiates and sustains the original error; what is the proper solution to it.
I ran into this exact issue after migrating a time machine backup from an older macbook air to a new macbook pro.
The following steps solved my issue:
1) Backup your current mac
2) Create a new user account on your mac, and login to that account.
3) While logged into the new user account, right click the time machine drive and select "get info" > Click the lock icon at the lower right corner so that you can make permission changes. Then Click on the "+" sign and add your new user account to the "Sharing & Permissions" window. Be sure to grant your new user "Read & Write" privileges and when you have done so, click on the down arrow and select "apply to enclosed items" This step will allow you to copy the library folder from your old user account to the new account without hitting any permission issues.
4) Download "TinkerTool" (An application that allows you to enable the viewing of any and all hidden files and folders on your local or mounted hard drives) and check the box that reads "Show Hidden and System Files" and then click "Relaunch Finder.
5) Lastly copy the Library folder from the older user account on the time machine backup drive to the new user's library folder. Also be sure to copy your Desktop, Documents, Pictures, and Music folders to the new account as well. Open Mac mail and follow the instructions to import the previous accounts mail messages. Once you receive future ics attachments or calendar invites you should be able to click on them and load the proper date and time within your iCal application.
This worked for me and I hope it works for you.