LCDs update 60 times per second (or more… 120 Hz displays are becoming more common) but they don't flicker the way CRTs used to, so there's no reason to think this would contribute to eye strain. Brightness could be an issue but you can just lower the brightness of the screen to match the surroundings.
As I see it the advantages of e-ink displays lie mainly in their visibility in direct sunlight and minimal idle power consumption.
Some displays do this as a feature though (known as backlight strobing, motion blur reduction, etc.): LCDs take time to transition, so if you keep the backlight on at all times, you'll potentially see blurring from persistence of vision while the display is mid-transition. Instead, you can turn the backlight off until the screen has transitioned and then turn it back on so that you never show a partially transitioned image.
Someone definitely flunked the messaging on this one, and I find it very disappointing :( The key advantage to an e-ink style of display is less eye strain, because you aren't staring into a bright light source that refreshes 60 times a second. (And battery life, of course; you can put your book down and forget about it until later). And that this limits the device is fine: a lot of people do a lot of reading! People like reading! Alas, as more and more people grow up reading all sorts of things on LCDs, so the inconvenience and the discomfort is just a normal part of reading for them, that becomes a much harder sell.