Open? Or is Money?
"By being open source, not only do the security problems get smaller – because of all the eyeballs on it – but the ability to work with new products grows."
Do they get smaller? If we look at the Debian OpenSSL disaster we've seen a major problem sitting at the very heart of the encryption engine yet it was undiscovered for over three years. And that's but one example, many open source projects have had issues (both big and small) which took their sweet time to be found.
What this theory is ignoring is that many eyes can still overlook the obvious. And I don't mean that in a negative or disrespectful way. But if you know a certain environment inside-out then the chances of overlooking obvious small caveats only increases. This is also why you usually let other (outside) people test your stuff. Open source doesn't change this concept at all.
Another problem is that not every user of open source software will actually look at the source code. And even if they do: with bigger projects you'll have several people working on it, who usually all have their own coding style. This only makes it more difficult for an outsider to actually grasp the whole code structure. It's the same issue with forking; although one of the major advantages of open source projects is that you can fork one to make it your own, forking isn't the thing to worry about: it's maintaining the new source tree, especially with those bigger projects.
So basically I see a lot of hollow marketing talk here. And that usually indicates commercial interests, which make me convinced that, as usual, the money factor is going to be the real winner.