On Android Chrome isn't open source at all. On Windows/Linux several key parts are closed source, that's quite a bit more "than a bit of Google integration".
Maybe "key part" is overstating it a bit, but the auto-update, crash reporting and usage tracking systems are all closed-source, as are the Flash plugin and some non-free audio/video codecs that are bundled with Chrome.
I think the auto-update, crash reporting and usage tracking code as well as the codecs are open source, they're just not compiled in by default in chromium builds.
If the source code is not available and it's distributed as a binary, by definition it can't be open source. (Plus some might argue about OSS licensing too)