Now I'm about as big of a fan of open source as they come, but I'm not sure if this is the proper course for cause and effect. I've done a lot of thinking about Linus' Law in the past few months as part of the Red Hat Product Security Team. What the Coverity report shows is that open source has fewer of the kind of defects Coverity can detect. That's really it.
On the topic of open source code quality and bugs though, I think there are a few more important things to consider.
1) The source code is available.
We've all written horrible horrible code when we know nobody will look at it. If I know someone will see my work, especially THE WHOLE WORLD, I'm going to spend a few extra minutes to make it look nice, which will help reduce bugs.
2) The original author is probably still around
One of the problems you can see with proprietary software is that the developers don't own the code. If a developer gets a new job, they'll probably never see it again. With open source, regardless of where you work, you're going to work on your projects. This "old knowledge" is a very powerful thing.
3) Anyone can help
If you report a bug to a proprietary vendor, they have to justify the fix from a business perspective. If the bug is obscure, or doesn't affect functionality, they may decide not to fix it. With open source, anyone can submit a patch. That means you can benefit from the long tail of contributions. The core 5% of people may write 95% of the software, but it's the other 95% of users and their 5% patches that can make the real difference. Those 5% patches are likely bugfixes, not new functionality.
4) The Distribution model is powerful
I worked for a company that write proprietary software once. The use and testing are very well defined. If a user found a bug because they were doing something weird, they were told to go away. With open source, there are hundreds of Distributions, all of them do things a little bit different. These corner cases improve overall code quality (a bug is a bug).
I suspect the overall message here isn't that Linus' Law works (it might, I'm not sure honestly). The message is that open source works. Why can't be pinned down to one thing, it's a lot of factors all coming together. Maybe all bugs ARE shallow with enough eyeballs. It's more likely though that the message should be "more eyeballs is better than less eyeballs".