If you are getting an error creating a Mailbox backup set then you will need to give the main Mailbox full permissions to all the Mailboxes.
Open up Microsoft Exchange Shell & run these commands to allow full access to all the mailboxes:
Set-User "%mailboxname%" -RemotePowerShellEnabled $True
Get-Mailbox | Add-MailboxPermission -User "%mailboxname%" -AccessRights FullAccess