This is indeed a PR disaster. Announcing something web based at this day and age with Firefox support as an afterthought is pretty stupid.
And it is another branding disaster. I disliked the Windows Media Audio and Video branding. I dislike the Windows Blah Foundation branding. And now I dislike the Windows Live branding. Why? Because it sends a confusing message. Is WMA and WMV only supposed to be available on the Windows platform? This seamed to be the case for Windows Presentation Foundation, so I thought I could live with it. But then at PDC05 Microsoft announced Windows Presentation Foundation Everywhere (WPF/E). If it is supposed to be available everywhere, why brand it with Windows?!
.NET suffered from serious branding misuse in the past. Remember every MS server product getting the .NET label stuck on it, even if it had almost nothing to do with the .NET Framework. Since then Microsoft has backed off from using .NET in product names. Did you notice it has even disappeared from the Visual Studio product name: it's Visual Studio 2005 and not Visual Studio .NET 2005.
Maybe Microsoft should completely drop the Windows term for the next version of its OS and just call it Vista.