"on your own computer" wording isn't applicable to headers-only clients

[JeremyRand]

dot-bit/index.md states:

instead of the phone book being a corporation or government, the digital phonebook is on your own computer. Bitcoin technology ensures that every user in the world has the same phonebook data on their computer, without anyone being able to illegitimately change that phonebook data.

This description seems to be inaccurate if applied to headers-only Namecoin clients such as the under-development Electrum-NMC. Is there a better way that we can phrase this, which emphasizes that users have the ability to verify the data autonomously (at least the DMMS signatures), without implying that the data is stored locally?