The FBI is talking out of its ass. What else is new?
There ALREADY IS A "SECOND INTERNET"!!
Hell, there are at least two, the Joint Worldwide Intelligence Communications System (JWICS for short, which Justice probably isn't allowed to use) that is not connected to the wider Internet. And the National Security Agency Network, which may (or may not) be connected to JWICS but also is not connected to any wider network. There are probably also more networks than that which are totally private.
The WikiLeaks stuff was all SECRET, you can route SECRET data over a system thats connected to the wider internet. With TOP SECRET information it cannot be, it has to be routed over JWICS or NSANET (depending on if its over a COMINT distribution or not) uses a dedicated network separate from the rest of the SIPRnet, NIPRnet and Internet.
Basically the FBI proposes to duplicate one of DISA's better efforts for the Intelligence Community. And they're going to get away with it because they'll scream "Think of the Children!!" and other such claptrap. They'll half-bake it, it'll half work, and when it gets breached it'll make all of us who are really in the community look like unprofessional dolts that work for Justice.
But we're all on the same team now, y'know. Which basically means they do whatever they want, and we'll get blamed for it when they screw up.