A primary goal of the Arduino project is that all of its parts work well together. You should feel confident that the Arduino software will be able to program your Arduino board, and that both will be documented on the Arduino website. To make sure this happens, we work hard to coordinate the development of the various pieces of the project. For example, enabling the automatic reset on the Diecimila required many careful modifications of the Arduino software and lots of testing; it was only possible because we share common goals for the project and are willing to work together to make them happen. Arduino's not perfect, but much of its power comes from its shared vision and coordinated effort.
To maintain this coherence and utility, we believe it's important to maintain control over what gets identified with the project and called an "Arduino". This lets the community have confidence that when they use an Arduino, they're using something that works well and works together with the other parts of the project. If anyone could call anything "Arduino", the name wouldn't be useful as a way of identifying anything. You wouldn't know if it worked with the software, if it could be used with the shields, if it would be documented, etc.
This doesn't mean that everything Arduino needs to come from us. In fact, another of our goals is to promote hardware designed by other people: helping to manufacture it, distributing it, supporting it with the Arduino software, and so on. We've done this with the XBee shield, which was designed by Libelium Communications and now appears in their SquidBee wireless sensors nodes. We're doing it with Leah Buechley and Sparkfun with a new wearable version of the Arduino. We hope to do it with a lot more people and products (if you're interested, contact us). We just want you to talk with us to ensure that your work fits well with the rest of things that go under the name "Arduino". Of course, we don't want to stop you from describing your work in relation to Arduino; so if your board "can be programmed with the Arduino software" or "is based on the Arduino reference designs", go ahead and say so.
Of course, we're not trying to imply that everything should be part of Arduino. If you want to create your own project, go for it. All we're asking is that you let us keep an eye on what happens to ours.
We're in the process of opening up our hardware designs and production files; I hope to have more to say on that soon.