I think that is advice to Merkins. In much of Merika, they can use tricks such as clear plastic to kill off most weeds by solarisation because they have a much hotter summer than us; as the site itself shows, it doesn't work in alaska. But even in the lower 48, I think solarising for a mere 4 weeks would be a bit short; people I have heard talking about this technique talk about leaving it for a whole summer.

Having had bindweed come up through the floorboards, I can assure you that the mere exclusion of light is not a fool-proof weed eradication method. There will be plenty of seeds and dormant rhizomes in the soil, so unless you succeed in increasing the temperature sufficiently to sterilise the medium (as in the solarisation technique referred above), you are going to have weeds come up next year.

Weed-proof membranes used as a long-term weed-excluding medium (as I use on my strawberry bed and my gravel path) are not water-proof like black plastic, because you do need water to go through. They aren't 100% efficient, but they do reduce the amount of weeding you have to by a lot.