My understanding is that the "green bags" allow the gas ethylene which the produce puts off to escape without hovering over the fruits and vegetables. Ethylene is one of the gases which promotes decay.
However, these bags do not prevent the nutrients from decay - just the appearance of decay. The produce continues to break down, but since ethylene is wicked away from the produce, it still looks fresh. So strawberries stored in green bags which look great after 9 days (and if they're supermarket berries, who knows how old they already were) might look and taste fresh, but be devoid of most nutritional benefits.
That is my understanding of the green bags after I did some informal internet research on them and on ethylene a few months ago, when I was interested in picking up a set. I've been reading a lot on freezer prep for foods, and one of the big promotions is of blanching for vegetables, precisely because blanching DOES temporarily arrest the decay of nutrients. So maybe blanching and freezing would be a better option than using green bags, nutritionally speaking.
(Please keep in mind that everything I just said is a blanket statement. Different nutrients and different produce are going to act differently, but in general, I believe what I've written to be correct.)