When you drag an email to a shared board that your team members have access to, in the back-end it inserts a copy of that mail into each person's mailbox.
If someone on the team accidentally drags an email to the board that they didn't intend to share, because it's been synchronized to other accounts, Sortd needs to be able to delete it from those accounts when they remove it from the board.
Without the permission to permanently delete an email like that, anyone whose mailbox it's been synchronized to would still be able to read it even after it's been removed from the board.
i.e. In short Sortd needs permission to permanently delete email to protect the privacy of all people on the team.