He seems to be setting a white background just to check the image against it as a means of seeing how it would look as a mounted print, or as a print with a wide border. That actually makes sense. I was under the impression the OP was suggesting you work with a white background... which wouldn't. Working with a white background will probably end up making you producing really light images, as what looks light on a darker background, will invariably look a lot darker against a white background. However, most people I know who are experienced printers, would just trust the RGB levels. A white computer screen is a light source... a piece of paper isn't, so in print, the contrast between the white background and image is a great deal lower. Swapping to white would give a rough and dirty check though. If the image is intended for online use however, then you'd check it against whatever background it will be shown against, because ultimately... that's how others will see it. If you just want the image to be accurate independently of background, then a mid grey background will give the most consistent results.
I would take issue with what was being said in the video though - namely that they are suggesting it's bad to set black and white points, and seemed to demonstrate this by merely reducing blacks and increasing whites in LR. Those are global, linear controls, and of course doing that will increase contrast and saturation. At no point do they use curves... which is odd, as that is a far more powerful and controllable way of controlling black and white points, and would allow a wider dynamic range without increasing contrast in such a linear way. Maybe they're saving that for another video (shrug).
