Does the Volmer (sp) Act specifically say that STATES can’t create such a database?
Yes, it tells the states that they can’t create a database either; see this snippet :
“No such rule or regulation prescribed [by the Attorney General] after the date of the enactment of the Firearms Owners Protection Act may require that records required to be maintained under this chapter or any portion of the contents of such records, be recorded at or transferred to a facility owned, managed, or controlled by the United States or any State or any political subdivision thereof, nor that any system of registration of firearms, firearms owners, or firearms transactions or disposition be established. Nothing in this section expands or restricts the Secretary’s authority to inquire into the disposition of any firearm in the course of a criminal investigation.”