I'm not sure where to start:
1. Tires are wear items and have different warranty provided by tire maker, not Toyota. It says so in the warranty booklet.
2. Road hazard, misaligmnent is not covered
3. Tire rotation helps to get even wear on all tires, since front and rear will wear at different rate (my rear tires last twice as long as front without rotation), it also helps with misaligmnent.
4. I would try to align the wheels first , most likely that's the cause of the problem or grabbing brakes (if the breaks grab very hard in one spot, the tire will wear more at that point and become little oval, making strange noise)
5. In my opinion lack of timely tire rotation should not create any problems on it's own, but it is legit reason to avoid warranty repair, unless you can prove some factory defect of the tire itself, but it would be hard sell now, after 19k. I don't think misaligmnent or unusual breaks wear would be covered either.
Either way you can call regional Toyota rep and see what he says, but it would good if you got second opinion and found real reason for extra tire noise, I'm not buying tire rotation all by itself. Which tires do you have? Michelins should last 30-40k easilly, I heard Bridgestones could wear in as little as 25k.
Disclaimer: I'm not an expert and all of the above is my best guess.