As long as 2 people can whomp a turret, having a pure AP is fine. Even Sony is secretly contradicting himself mentioning Kassadin, who is dog poop against turrets.
The whole point of magic damage (aside from forcing people to split their resist type) is to be a little better vs. champs at the expense of being a lot worse vs. turrets. If you roll with a strong AP component in 3v3, it's mainly a matter of farming and waiting for the enemy to slip up. Defending turrets is easy as pie because of the aforementioned fast time to move to another turret, and they can't defend a turret if they're dead.
The best TT teams I've seen had about a 50-50 mix of both, just like in 5s. The whole idea that you can consistently backdoor in TT if you're fast enough - without any nuking the enemy back to their base for heals - assumes a reactionary rather than predictive defense, meaning it'll only work until your elo gets high enough that people will recognize openings that big in their own defense before you do.
You need a lot more focus on tanking, and there tend to be a lot more off-tank ADs than off-tank APs, and this may be what throws off your intuition. It's like people who play "AD teemo" who are actually playing a crappy AP teemo because they don't notice that they sure have a lot more AS than most typical AD builds and oh hey look that just happens to synergize with his poison passive!
