Anivia and Crits

I remembered how a little while ago a Rioter mentioned that Anivia's and Ashe's critical strikes were still considered crits and that's why they didn't affect Dragon or Baron. Something along the lines of "For all intents and purposes, Anivia gaining double damage on her E is considered a crit"

Yet I just tried out Warlord's Bloodlust for the heck of it, and I noticed that dealing the double damage on her E didn't process the mastery. Indeed, Infinity Edge also didn't increase the damage from 200% to 250%.

What gives? It's considered a critical strike "for all intents and purposes", except when it would actually benefit Anivia or add some fun just for the heck of it. :/