Total information is not the same as informative labeling. Companies are not allowed to label the absence of irrelevant things for good reason--when a food is labeled as "X-free", X should in some way be something worth avoiding for some people (if you want a trans-fat-free / carb-free / gluten-free diet, etc.) This is what consumers expect when they see a label advertising the absence of something--that it is worth avoiding.
If you are allowed to put completely irrelevant or misleading labels, companies could "distinguish" their brands with other nonsense:
"Biotin free!"
"No added Niacin!"
"No synthetic Pyridoxine!"
Does any consumer realize that these are in fact not things you should be avoiding? Of course not, and they shouldn't have to. So if you start letting companies label food as GMO free, most people will be misled because they expect the labeling to be because of a scientific reason the food is worth avoiding--when there is of course absolutely no scientific basis to fear GMO foods.