I got the notice too, in fact, I just got four copies of the second notice that went to the junk folder. Although I do have an iPhone 6 from December 2014--still on the original battery--it must be a miracle, although I don't use it as much as most people who have only a cell phone and no land line, use it for work, and also use it extensively for streaming an Internet. Anyway, there is a clause in the form you fill out to make a claim that you are declaring under penalty of perjury various things, one of which is that you suffered diminished performance. I believe at that time my battery was over 95% of design capacity, and the throttling only occurred when it got somewhere below 95%, so I never experienced it that I could tell (it's currently at 91% according to the iPhone info, but when I hook it up to Coconut Battery on my MacBook about nine months ago it was a few percentage points lower; I'm not sure which is more accurate). I would wager than Apple has records of customers' iPhones' percentage of design capacity, and knows whose phones were throttled and whose weren't, so that could be a trap, although I doubt they would pursue it.
A few years ago, out of the blue, I got a physical mail notice on a card of a class-action lawsuit proposed settlement with an auto maker for recording phone calls to their customer service number but not telling people they were recording them, which in my state is required by law. I had called that number a couple times within the last month or two of the six-month time frame in the lawsuit. I called the law firm involved and talked to one of their attorneys who informed me that the settlement was a fixed amount and how much each person got depended on how many people filed a claim--it could be anywhere from $75 to $500. I had a feeling that not many people would bother to file the claim, so I did, and a few months later I got a check for, $447. I don't know who instigated that lawsuit, probably some insider who contacted a law firm, but it was like found money to me, and of course the lawyers made money. That same auto company had, a bit earlier, created a voluntary program to compensate customers for incorrect mileage information for some of their cars, including the one I owned, giving them rebates based on mileage for the difference in the average cost of gas they would have paid if the car got the mileage stated. The program lasted as long as one had the car and would also be available to subsequent owners, as it theoretically affected the value of the car. By signing up for that program you waived your right to sue them over the issue, so it was a smart proactive move.