Here's my take: a backlit LCD very easily can cause more eyestrain than an E-Ink screen simply because of the backlighting.
I don't believe there's any significant disagreement with the idea that reading from a screen that's brighter than your surroundings is hard on the eyes for many people. Because E-Ink works entirely on reflected light it - like a paper book - is not going to be brighter than the surroundings unless it's being directly illuminated. This is not the case for a backlit LCD, which can easily be brighter than the room.
Another factor to remember is that the majority of complaints about LCD devices aren't directed toward reflective LCD devices such as the Jetbook. Complaints about the Jetbook have historically focused on points like value for money, format support and battery life - not eyestrain.
LCD displays may not directly cause eyestrain, but enough people have issues with backlit LCD devices that it is something to consider when looking for a new device. But as always, the best option is to look at something first, before buying it so you can decide what meets your needs.