In order to process uncoupled PST files which are assigned to other users, the PST Enterprise service account requires Full Access on the PST file owner's mailbox. These rights can be assigned using the following PowerShell command:
Add-MailboxPermission "OwnerMailbox" -user "ServiceAccountName" -AccessRights FullAccess
where OwnerMailbox is the PST file owner's mailbox, and "ServiceAccountName" is the PST Enterprise service account.