Android is not Google's OS any more than Linux is a Red Hat OS. It is an OS produced by 78 different companies who are members of the Open Handset Alliance and also has numerous unaffiliated contributors.
Android is developed by Google behind closed doors. I am unsure of whether those other companies work with it behind those same closed doors, or not. But it's development is controlled by Google in a way very unlike Red Hat's development of Linux (or RHEL).
You can take the released Android code and use it however you want. But practically speaking, Google still maintains a lot of control through the closed-doors development model. So it is fair to say Android is "Google's OS", but I would agree that that can be misunderstood to mean proprietary (which the released code most certainly is not), so maybe it's a bad choice of phrase.
As I said before, I don't know if the other companies work with Google behind closed doors on the development - the development is behind closed doors, so we can't tell. But even if they do, it's still controlled by Google. For practical purposes, if you want to launch a device with Android, you need to partner with Google - only that way can you work on the latest code, and be aware of features in development, so your product when it finally launches will not use an outdated OS.
Kudos to Google though for open sourcing it, when they do release it into the world. I am not saying Android is bad or anything. Just that it is controlled by Google. I'm a fan of Android myself.
Regarding the story itself: Google is 100% right. Patents apply to 'specific machines', or should according to the law, so Google should be free to develop software free from worry from patent lawsuits. Hardware companies may need to enter patent agreements for their specific products. Google is arguing for a model of patents that makes a lot more sense than the one currently in practice in the US, and it happens to be the one that is on the books, so hopefully Google will prevail.