The fact is that an end user should not care if software downloads a "binary blob" without running it. This is functionally equivalent to downloading anything from the Internet, a JPG file for example. Chromium downloads a bunch of things on startup, and nobody seems to mind. Just because hotword.nexe happens to be an executable blob doesn't really make a difference.
Is that the official position of Google? Reminiscent of when Thomas Hesse from Sony stated: "Most people, I think, don't even know what a rootkit is, so why should they care about it?"
Great point. Sure, I get it. By that logic, sending me a mail bomb (and of course, not activating it, because I mean who would do such a thing after painstakingly creating it?) is the same as sending me flowers.
Whether or not people should care, some people do care. If Debian has to edit what you distribute to remove proprietary parts of it, you're probably not distributing something that is open source (which means 100% open source).
I understand the concern that a proprietary component may be performing unknown instructions, and indeed Chromium does download hotword-x86-64.nexe on startup, but it has been carefully designed as an opt-in feature. If you do not turn on "Enable "Ok Google" to start a voice search" (in chrome://settings), Chromium will not run the plugin. You do not need to trust Google engineers to tell you this; the open source Chromium code has the logic to decide whether to run the plugin.
I have posted a detailed response (including the link to the place in the Chromium source code where the module gets run) on our bug tracker at http://crbug.com/500922#c6.