**Scenario:**

In our world, only statistically significant ($p<0.05$) results are published, everything else is rejected or not even handed in.

Let's now assume an experiment is $100$ times conducted and in truth $H\_0$ holds.
Since the $p$-value is uniformly distributed under $H\_0$ (let's assume all conditions are satisfied) this would mean that on average $5$-paper could be handed in which all claim that they have found a statistically significant effect ($p<0.05$) and the academic world might actually believe in the alternative hypothesis $H\_1$ although $H\_0$ is actually true (of course no one would actually know that).

**Question:**
Is this reasoning correct? I wonder how this reporting bias is called, it's different from the [publication bias](https://en.wikipedia.org/wiki/Publication_bias) (or just a consequence and that's why it has name of its own?).