That's partially correct, and then other parts like the sticker are obviously overexaggerated. Why? Because of the federal Magnuson-Moss Warranty Act it's not as clear cut as you describe. And I think the correct information is important to delineate.
Certain aftermarket parts are prohibited and protected by law, meaning the manufacturer cannot void a warranty based of the customer using aftermarket parts with some exceptions, say like custom taillights. Obviously if those fail it's not the responsibility of the manufacture to cover a part that isn't there's, that responsibility goes to the manufacture/warranty of the company that produce the aftermarket part. Here's the catch, if those taillights cause broader electrical damage to the vehicle, that damage will void the warranty for the particular areas affected, it WILL NOT (again, by law) totally void the warranty for the rest of the vehicle that's covered. This is an important distinction for people to understand.
HOWEVER, modifications to the engine of any kind, including even just a custom intake like you have here will in fact void the entire powertrain warranty should the specialist at dealership decide your part led to greater engine failure, BECAUSE Toyota will not cover any repair that caused the vehicle to operate (and fail) outside of it's designated operation set at the factory in terms of powertrain.
You're only saving grace at that point is that maybe the specialist at your dealership either won't catch it, or they won't report it to Toyota as such cause. You have to remember, dealerships are NOT Toyota, they're independent franchises that invoice Toyota for the repair bill, so it's also in their monied best-interest to accumulate that billable work. That being said, the reporting for repairs the dealerships are responsible for is pretty rigorous and scrutinized by Toyota. So it's Russian roulette.