This seems fundamentally incorrect to me. Wouldn't research all around just fail if no one ever reported their negative results, thus dooming many other researches to performing the same fruitless experiments?
Let's say that you only publish when you discover an effect with a p-value of better than 0.05 -- that is, when you believe that, if the effect weren't real, then the probability of observing an effect at least as extreme as the one you got has less than a 5% chance of happening. This is pretty typical.
Let's also say that you and 19 other groups are studying an effect that isn't real: the hypothesis that meditating on pink unicorns will get rid of skin cancer.
By (perfectly reasonable) chance, 19 of your studies reject the Pink Unicorn Hypothesis with p-value = 0.05, and one accepts it -- i.e., one group gets a result that should have happened 1/20 times or less if there is no Pink Unicorn effect.
Since the first 19 groups are silent, and only one group publishes, the only thing we see is the exciting announcement of a possible new skin cancer cure, with no hope for a meta-study that notices that this actually the expected result given the null hypothesis.
So yeah. That's bad.
It does (rarely) happen in Physics where everything is expected to be repeatable, and results from one experiment carry over to similar experiments. It almost never happens in medicine, where the bar of acceptance of a hypothesis is already ridiculously low.
If you don't have a reason for the failure, just "hmm, didn't seem to work", you can still publish, but it's harder. The next-best case is if you have a large-scale study failing to find a result for something that many other people have claimed should exist, e.g. power-line cancer studies. But if it isn't in that category, it's harder. The fundamental problem is that nobody wants thousands of paper saying "X doesn't cure cancer. X2 also doesn't. X3, once again, does not cure cancer", because the vast majority of Xs don't do Y.
He chose to publish one paper, fittingly, in the online journal PLoS Medicine, which is committed to running any methodologically sound article without regard to how “interesting” the results may be.
edit: though looking at the site, it doesn't seem to present itself with that motivation. It also costs $2900 to publish an article, so there's some financial hurdle to publishing.