Let's take this a bit more carefully and discuss the assumptions in both the question and the answers.
My assumption is the data from the first trial is indeed accurate and representative. You may argue that and if fact I think that is what you are arguing. If I understand what you posted you are saying that another trial might come up with different results because it is a different trial. That argument is basically based in the p<0.05 having a possibility of coming up with a different answer from the 5% random sampling possibility.
I'm arguing that another trial with a larger n can detect a smaller change in the primary variable with statistical significance than a smaller trial can. In fact with a very large trial a very small change in the primary variable can be detected with statistical significance. This is generally described by the use of the descriptor the power of the trial.
If there is in fact a real signal in a small trial that is swamped out by the random variations in the placebo response, a sufficiently larger trial will show that signal real signal statistical significance.
If there is no there there, it doesn't matter how much larger the trial is, it will not show statistical significance.