The only benefit of choosing a white background over a light grey background is that it arguably gives you a broader range of text colours that you can use, and still remain within accepted usability and accessibility guidelines.
In other words, if you want to use blue text you would be able to use a slightly lighter shade of blue on a white background, than on a light grey background.
It's also important to keep in mind that the colours perceived on users' screens vary based on the gamma settings on their screens (especially important with the new release of Night Shift on iOS (New in version 9.3: http://www.apple.com/ios/updates/), and also based on the environment they are in.
This last point is important to this question because in bright sunlight, on a mobile device, the white background paired with very dark text could result in a better reading/viewing experience because you actually need the brightness on the screen to be as high as possible.
I think your point about a benefit of the light grey screen being that you can use white as an accent is problematic. Whilst your accent is not text, you still of course want it to be noticeable, but the contrast between a very light grey, and white, might well be too little for your accents to be helpful and accessible.
There's also then an aesthetic aspect to this. Of course within reason it is beneficial to have an aesthetically pleasing UI, because it is both perceived to be, and ends up actually being easier to use (barring any actual usability issues of course). The User Experience comes out of not just the UI, but also the emotional reaction to it, and to the brand of the product, and to the beauty of it. White backgrounds arguably are more compatible with a wider range of colour schemes (that would be used for graphical features, text and branding), and currently I think personally that the connotations of white imply minimalism, simplicity and beauty more than light grey (overall..I know that is very debatable :) ).
Here is a helpful colour contrast checking tool, by the way: http://snook.ca/technical/colour_contrast/colour.html#fg=33FF33,bg=333333