Her passive requires at least 3 spell casts to charge (none of which can be her E), and then a large wave to heal more than 1 segment of health in early-game. Even with a rushed aggro build (luden's, boots, Morello, I still only get around 10-20 hp per hit. That means a single wave gives a maximum of 2072=280 health, so 840 health over 3 waves. Assuming that all 3 are cannon waves (an impossibility) and that I hit all 7 minions in each wave with my Q on both hits, AND that I manage to charge her passive on each wave before the next one shows up (impossible, since I'd have to get off 3 Ws on the nearly-dead minions while I, myself, am SUPER weak, and probably with no ult). This all means I am certain to be out of mana, even if I have three rings and mana regen quints, and I farm perfectly. The wiki tells me that, without items, masteries, or runes, Ahri will have 1054 HP at level 9, and 11.4 points of mana regen (that's over 5 seconds. So you're looking at about…2.1/s. Base, of course). So it is literately impossible for her to have healed to full from 20 HP by her passive. And her mana would be so low it would have to be negative. Even blue buff, at that level, wouldn't make her able to spam her spells near fast enough to heal at that rate (It is possible to heal from around 200 HP at end-game, if you have enough AP, by discharging your passive on a wave of 30+ minions. But you don't lane at end-game, and her late-game has a clear weakness, so I don't think that's what you're talking about). Nor would it give her more than half of her mana back at the most, over that time.
All of these are facts, taken from either personal experience or the wiki. So, sir, stop lying.