I think you need to learn more about open source, it's pure transparency, how can a project be open source and still have a backdoor? And no one sees the back door? What's the open source then?
Open-source projects have nothing to hide, you can easily see all their codes and what they are running, with no hide-and-seek like Closed source, what you just defined sounds exactly like Closed source projects.
That's mostly true, but knowing how complex code can be depending on the project, the developer can easily have an obfuscated backdoor in the source code. It'll take a very competitive developer or a developer that's specifically looking for such an exploit/backdoor to spot it.