How will this affect the branding of the product? It is, after all, the hardware partnerships that will help define how Chrome OS is presented to the end user. There's nothing to stop someone from installing Chromium OS on their current netbook or notebook -- but such users are not the intended market, and Google is not getting bent out of shape about that. If anything, it's a win for them: the more people running Chrome(ium) OS, in any form, the better.
A third, and extremely major part of the whole package, is how offline access is going to be handled in the finished product. It's not clear whether that's going to be handled by things in the base package, or by components which are primarily Google-branded, and not available as Chromium OS (as opposed to Chrome OS) pieces. Right now little, if any, of this plumbing exists, and that alone is a good reflection of the very alpha state of the system. If Google leaves too many of the key parts of the Chrome OS experience to be filled in by its nascent developer community, that will clash badly with its plans for delivering a solid end-user experience.
The real test of Chrome OS's draw will come when users are invited to pay money to experience the product at its best. If its best turns out to be little better than what people can experience for nothing on their own hardware, then it will remain as a niche within a niche. It'll be worth keeping an eye on both Chrome OS and Chromium OS in the months to come, if only to see how the project and the product both merge and diverge.