I don't think it's a myth, but I do think it's been exaggerated. It has suited the makers of e-ink devices to draw attention away from the drab grey-on-grey look of e-ink by advertising that it's easy on the eye. Why not - it's a good marketing strategy - but it doesn't mean that we'll all get eye trouble if we don't use their products.
I've been reading on computer screens on a daily basis for over 20 years. I've used them for work, to play games, to read email, search for information, and so on, for hours on end with no eye problems at all. That doesn't mean that some people don't have a genuine difficulty, just that I don't.
However, I also remember that when computers first came into widespread use in workplaces that a certain percentage of people claimed that they were giving them RSI. It was quite the buzz for a while. Yet you hardly hear of it now, despite the number of users having greatly increased since then. This is probably partly due to better workplace practice regarding sitting correctly and taking movement breaks. The same appears to be true with eye strain. Some people really did get RSI and some really do have eye problems, but the millions of hours now successfully worked at computers every day now suggest that the numbers whose problems can't be solved by changing their settings or usage patterns are relatively small.
I actually prefer a properly adjusted backlit screen to the rather dull look of e-ink (although either is OK) so the rapid development of small tablet style computers is perfect for my needs.