If they got a statistically significant result given some alpha value, then that's a valid result, assuming the experiment itself was set up in a valid way (random sampling, controlled, double blind, etc.). Statistical significance tests take the sample size into account. A large enough difference can make up for a small sample size, and vice versa.

The Valkee company is financially backed by ex-Nokia execs and other people with money and influence in Finland. They have the means to get a small University in Northern Finland to make a study in their favor.

There have been interesting studies about light sensivity in the skin, so why not the brain. However, this study doesn't really prove anything.

Also, don't underestimate the value of placebo in the treatment of mental ailments.

Often its for a good reason for instance when looking at the effectiveness of a surgical procedure in a sub-group or the treatment for a reasonably rare condition. Sometimes it is because of the need to use a random or carefully selected bias group.

But, as a one-time criminologist's statistician used to samples in 1000s (or 100s at least), I have often concluded that it was just bad science.