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 (or just a consequence and that's why it has name of its own?).