I'm not sure that's right, if the "z"-pronounciation is for verbs. I would think the Department of Housing is talking about "housing" as a noun, rather than "housing" in a verby-way. Like the "department of transportation". You can transport something, but you don't transportation something. Or "Department of Education" isn't educationing people, it's educating people.
> I'm not sure that's right, if the "z"-pronounciation is for verbs.
It is right. The rule you are stating is an overgeneralization; it is correct for specifically distinguishing the verb forms “house” and “houses” from the singular and plural noun forms “house” and “houses”, but not really otherwise (maybe by derivation, in that “housing” is “that which houses”, but...)
Bastard language this is.