True. My point was comparing IPv4 with a native address vs. IPv4 through a NAT.
Taking your story backwards, if the FBI intercepted messages with ISIS and recorded the network information:
Using a real IPv4 address: They get the account name and address from the ISP, then get a search warrant to find evidence and determine who in the home is the culprit.
Using a real IPv6 address: Same as above, only now they may be able to tell which computer in the house was used, making their job easier.
Using a NAT IPv4 address: The ISP is unable to tell the FBI which account is associated with the IP address. The FBI has to use other techniques to eventually determine who the bad guy is.
Of course, in the above example, the NSA would likely have a box inside the ISP that logs everything interesting, but if instead of the FBI, it was the RIAA, MPAA, or someone like that, they would be stumped.