While a small study is more likely to be wrong, there are two corollaries to that. The first is the second point raised - effect size. If (to take the extreme case) you have a study of three people who are all eighty years old and in a persistent vegetative state, and you give them Wundadrug, and they all wake up and suddenly look thirty years old, then you don't need a much larger trial to see that Wundadrug is almost certainly doing something interesting.

More importantly in this context, they're easier to replicate. If a study involves a hundred thousand patients over a thirty year period, then realistically nobody is ever going to check to see if they can get the same results. If, on the other hand, it involves ten patients for two weeks, anyone who is interested enough can try to replicate it with minimal effort.