Heartbleed and Shellshock, the two most significant vulnerabilities found in heavily used open source software, were found by vulnerability testing and not code inspection. So while being open source is a nice-to-have attribute for a piece of software, that's as far as it goes. Painting open source as being a magical wand that wishes away all our security troubles is completely out of order.
Edit: I'll go further. It's become dismayingly apparent that very little systematic code review of open source software in order to secure it is actually taking place. It now seems quite possible that the most thorough investigations of software vulnerability, via code analysis or any other techniques, are carried out by those wishing to exploit them. They are well funded and highly motivated. Looked at in that light, the balance may well tip towards open source actually increasing the likelihood of software vulnerabilities being exploited maliciously.
The open source community has a long way to go if it's going to clearly demonstrate that it's model is advantageous, and complacent pronouncements of it's assumed superiority like this aren't going to achieve that.