A good backlit screen, set to the proper brightness and contrast levels, should not be visibly "backlit"! If it is, your screen is too bright and you will strain your eyes.
This is the main issue right here with using backlit devices for reading - most people (including many here on Slashdot) have no idea how to use them properly.
In a normally lit room, my monitors and other LCDs look like a piece of printed paper (provided they're displaying black text on a white background, of course), because that's the way I like it. No eyestrain whatsoever