HP is one of the few companies making the Chromebox. In fact, in the marketing pitch of the product itself, they claim that "the fanless design prevents dust from being ffunneled through the computer case". According to a teardown, there is infact a fan and it is not silent and it will pull dust into the PC. So either the marketing team didn't know what was going on, or they are just plain lying.
Given that the Chromebox is powered by a 17W CPU it was unlikely that it would be fanless, so it's interesting to note HP marketing it as such.