"Eye strain" might be overly dramatic, but certainly fatigue will happen earlier in bright contrasty reading conditions. Designers often want pure white backgrounds though, they love their white backgrounds! So the only improvement possible is to increase the text from #000 to something like #222. This does not mean the text won't look black anymore, it simply takes the edge off but still looks black. Obviously the lady's blog she wanted grey so she went with #444.
Ideally though pure white background should be avoided if there's pages and pages of text to read. "Paper white" is what e-readers aim for. Thank God the Kindle app for tablets allows background colours to be reduced. I like the "newspaper white" tone, with a touch of sepia thrown in. Perfect!
#FFF text on #000 background is the worst. Many designers I've worked with over the years agree. Paragraphs of text will "shimmer" due to the extreme contrast. If there's a lot of text on the page, never have it #fff on #000. Bring the white down a notch and/or the black up a notch. It will still look like white on black but just look softer and better.