This is false. If you run a programme that is open source that is insecure the fact that it is open source doesn't help you. The only thing that helps you is if someone fixes its flaws. A project being Open Source is not a panacea or guarantee of any kind. Also, source being viewable does not immediately imply that others can implement other versions without a license.
Back Away from the Bitcoin Barbed Wire

I don’t think there are lot of people who think open source is/could be/would be/will be safer because.. .it’s open source. At least I have never seen anyone claim security comes from the license or visibility of the code. Now some people do think that those thing can make a difference because:

Maybe your stuff is out there in the open, no releasing sub par stuff, your name is on the line. People will see if you go full retard and might call you out.

Maybe this project attracts people with different areas of expertise and these people can bring their contributions. The model can allow anyone to just submit a pull request and ideally the best implementation would win.

So, just the fact that it’s open source does little if nothing to guarantee any degree of security. But at least you have the opportunity to see if it sucks. You have the opportunity to validate what you run. So even if open source doesn’t guarantee any level of security, it does enable you to make better decisions about what you run. So at least open source can enable more secure systems.

Open source might not make software more secure, but people do and I think many people claim it enables better people and ideas to rise to the top. How often that happens, I don’t know of any studies but then again, the alternative of closed source is not any better and at best gives the exact same guarantees of security.

Shitty developers create shitty code. Complicated software can have security issues even if it was done by the elite of the elite super duper programmers.