Council of Elrond

Are the White Tree and Stone of Erech permanent events discarded upon leaving their corresponding sites?

These cards say they are "playable at" in contrast to other cards that are explicitly discarded upon leaving (e.g., Houses of Healing and Hall of Fire) which also state that they are "playable on" a site. There are a couple netrep rulings regarding Wizard's Trove with White Tree NOT being discarded when leaving the site. But I haven't seen anything regarding Stone of Erech or White Tree alone.

White Tree with CoE Errata #13 wrote:Unique. Sage only at Minas Tirith. Playable only if you discard a Sapling of the White Tree borne by one of your characters at Minas Tirith, or one from your MP pile stored at Minas Tirith. Minas Tirith becomes a Haven [ ] for the purposes of healing and playing hazards.

Stone of Erech wrote:Unique. Playable at the Vale of Erech and if the Men of Lamedon are already in play. Discard if the Men of Lamedon leave play.

VS

Hall of Fire wrote:Playable on a Haven. Any company at this Haven immediately following its movement/hazard phase may choose for one of its characters to untap or heal (from wounded to tapped). Discard Hall of Fire when the site card is returned to the location deck.

Houses of Healing wrote:Playable on a Free-hold. Site becomes a Haven for purposes of healing. Discard Houses of Healing when the site is returned to the location deck or discarded.

There is no reason to discard them (White Tree / Stone of Erech). These phrases specify when the events may be played. Permanent events are normally only discarded for reasons stated on their card, or "When a card is discarded, so are all permanent-events on that card."-CRF, but as you noted these two cards are not played ON a site.