If the recipient of the notice appealed on day 13, he might struggle to run an argument that the claimant cannot prove the notice was delivered within 14 days.
If the presumption that a notice sent by post (PoFA itself doesn't specify first class post) can be rebutted, I would suggest it can be rebutted both ways (ie, if the sender can show that it was received sooner than that, by, for example, showing that the appellant appealed before the presumed delivery date and therefore must have received it sooner).