Question to clear up my confusion about the LB/IBG thing on Surrender@20

Lich Bane and Iceborn Gauntlet Interaction When asked how the interaction between owning both Lich Bane and Iceborn Gauntlet work as they have unique passives that do not stack, Xypherous noted: "So, for passives that don't stack - we try to come up with some kind of set favorable interpretation of which aspects of passives for you. LB generally has the highest single target damage - so it gets applied as your single target. IBG should apply the AoE slow and applies physical damage in that area. If you have Tri-force and IBG, Tri-force gets used as the single target but IBG AoE still applies. Likewise, if you somehow have Archangel's staff and Manamune, you'll get 8 Mana on spellcast and 4 Mana on Attack. It's the most favorable interpretation of the passives you have."

Copy pasta straight form the site.

So if i'm reading this right if you were to own LB and IBG the bonus damage proc would come from lichbane instead of Iceborn but still granting the AoE slow?