Found this on a Logmein Community Forum and it was posted by joshopkins (props to him):
The Operator or Administrator has refused the request (4320)
Error 4320 signifies that a non-administrator is trying to log in with a Windows username and password that does not have permission to use LogMeIn. To allow a non-administrator to use LogMeIn, you need to specify access rights for that particular user account.
Once connected to the target computer as an administrator (the computer you want to access remotely):
If you are using LogMeIn Pro, go to Preferences > Security settings > Access Control
If you are using LogMeIn IT Reach, go to Security > Access Control.
Please note: To get to the LogMeIn Menu screen or the Dashboard you may have to log in as the Local Administrator to the computer when you open LogMeIn locally and shown the blue authentication screen.
Then click on Add > List Users and Groups, and find the user for whom you wish to specify permissions.
Edit the permissions on the right side of the page. The options will explain themselves if you move your mouse over the checkboxes.
Once a user has been added with at least login rights, they will be able to access the target computer by using the non-administrator username and password.
When you setup users in Access Control, you can give them full control or set specific permissions. If you wish to give them only certain permissions, then you should leave the boxes in the "Configure" section unchecked. That way, the user won't be able to change any LogMeIn settings in Preferences.
I am in a Domain, can I make this easier?
In network environments you may need to setup user access on multiple computers. The Access Control settings are stored in the registry. They can be transferred if they contain only users/groups whose SID are the same within the domain. One such a group is the Builtin/Users, which might fit for their needs. The settings are under HKEY_LOCAL_MACHINE\SOFTWARE\LogMeIn\V5\Permissions. Follow the steps below to export the registry key to other computers:
Go to a PC, set up the necessary access control permissions. You can list the available domain users/groups on the page, use those.
Export the above registry key from the PC
Optionally, set up the same settings on a different PC and check if the registry settings are the same
Deploy the exported registry settings to all PC.
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