What is important is how the OS interacts with the user. This is where Apple shines. This is also where Google is looking to shine as well. If the user experience can be provided entirely within the browser, why not?
Because it is readily available in free form, it is no longer important, significantly or otherwise? Seriously?
Yes - it's become more commoditised. No, you can't just "replace" it with a browser. And yes, there is a qualitative distinction in degrees of hardware support and underlying engineering.
But you are right, you can't replace an operating system with browser. However, you can treat the OS as just another layer in the stack in between the network card and the browser. It's even an interchangeable component -- swap out Linux or Windows or OS X and you have still have something that can push bits onto the net and run a browser.
As far as the user experience goes, non-Windows systems are still handicapped by hardware and software compatibility issues which are decreasing in relevance, especially for a hardware vendor who can ensure that at least the hardware it ships is fully supported in their OS of choice.
Sure, web apps and AJAXian techniques may be putting a dent in domains formerly owned entirely by standalone desktop GUI apps.
But your browser is not going to implement your hardware device drivers, I/O subsystems, network stacks, filesystems, and, well, ${insert very long list of other ways in which the OS interacts with the fundamentals of the machine}.
To say, "Ah, well who cares, it's all about the browser now anyway" is really, really missing the point. Maybe Google Docs displaces Microsoft Office, but do you really think you're going to XMLHttpRequest your SATA driver, process scheduler, or IP routing FIB (forwarding information base) away?