Since 2012, Amazon's high-end Kindles (the 2012 Paperwhite, the 2013 Paperwhite and the 2014 Voyage) shine light directly into the eyes. It looks just like a backlit display although technically the light and the diffusion panel are in front of an opaque (e-ink) display, not in back of a translucent (LC) display. On my Paperwhite, it is impossible to turn this light off -- only to dim it.
Also, I dispute the OP's contention that reflected light on s paper book is any better; certainly, a normal bed-side lamp is worse for the sleep of anyone sharing the room with the reader.
EDIT. Although like I just said, an iPad probably has less of a deleterious effect on sleep than a Kindle Paperwhite does, it is probably possible to do better in the current market. Specifically, Samsung makes a tablet (the Tab S, which comes in 10.5- and 8.4-inch versions) with an OLED display, which has the advantage over LCD displays that the portions of the screen that are supposed to be black do not emit any light at all. Especially if used with software that displays red or orange text on a black background (to minimize the blue-ish photons) an OLED display is the best choice in the current smartphone-plus-tablet market AFAICT if protection of sleep is the main consideration.
EDIT. Oops, I forgot to include my main reason for preferring the iPad to the Paperwhite: on iOS, Settings > Accessibility > Invert Colors reverses black and white. Combined with the fact that many iOS apps like Safari and iBooks normally present a white field broken only by text and thin lines, the use of "Invert colors" probably results in less light entering the eye than a Paperwhite since (unless they changed it since I last updated the software on my Paperwithe a couple of months ago) you cannot alter the Paperwhite's default color scheme of black text on a white background. I will concede that the Paperwhite's brightness setting goes a lot dimmer than the iPad's does, but I consider that consideration to be trumped by what I just wrote, and, again, neither Paperwhite nor iPad comes close IMHO to an OLED display used with decent software.