Not true.
One of the most difficult courses I took in college was Stats for Psych. I took with a professor who worked with other professors to design their studies, so he was a very good source for what could be considered significant. He specifically talked about this issue of small trial sizes and explained that a trial on as few as 6 subjects could produce significant results.
I really loved the course and how it helped me to understand the results of studies much better.
