I've heard people discussing this, so I thought I'd chime in with a few thoughts.

1. Right To Exclude vs. Right To Use: First, remember that owning a copyright means having the exclusive rights (minus whatever rights you've licensed to others, and whatever rights they may have under fair use and other doctrines). The copyright is thus the right to exclude (and therefore the right to sue). Even those who don't own the copyright may have the right to use the work, because they have license, because they are entitled to under the fair use doctrine, and such.

2. Ownership of the Right To Exclude: This having been said, who owns the copyright? The initial owner was the killer himself. If he expressly conveyed it in a signed writing during his life (e.g., wrote to NBC that "I am conveying my copyright to you," and signed the writing), then the copyright is owned by the recipient. But if he didn't convey it, and didn't mention it in any will, then the copyright is owned by his parents (since he doesn't have a wife or children, and his parents are thus his heirs). I haven't heard of any express conveyance, so that means the parents own the copyright. They might be able to sue people who distribute them, copy them, or run them, but they'll lose if the defendants have a license from the killer or are engaged in fair use.

NBC thus can't sue anyone who copies the materials from its broadcast or its site, unless they themselves have added some creative expression (which may include sufficiently detailed editing decisions) that is being copied. They simply have no rights to sue over copying the killer's work (again, unless he conveyed the exclusive rights to them in a signed writing, which seems unlikely).

3. Implied or Express License as Limitation on the Right To Exclude: The killer's sending the materials to NBC likely conveys to NBC a nonexclusive license to use the materials, probably including on its Web site. The killer's family thus can't sue NBC to stop it from continuing to distribute the materials.

4. Fair Use as Limitation on the Right To Exclude: But in any event, these are materials that are of pretty substantial public importance (whether or not you think it was ethical or proper for NBC to distribute them). I expect that the parents would disclaim any desire to profit from them, and if they sued they'd sue only to suppress them, so there's no effect on the market for the materials. And even if NBC has some copyright in the material it added (for instance, a logo in the corner of the screen), its additions are likely very modest indeed.

So people who want to copy the materials would have a very strong fair use defense against both the killer's parents (should they wish to sue) and against NBC (should NBC sue over use of its very modest additions to the materials). I'd say this is so even if they copied the entire materials, which usually cuts against fair use, but here would likely be outweighed by the other factors.

5. Exotic Arguments: Might the killer have deliberately abandoned his copyright by releasing the manifesto with the intention that it be distributed as widely as possible (presumably the goal of manifestos)? He's dead, so we can't be sure of his intention, but it seems likely that he did have this intention. This, though, is likely not to matter much, since the fair use defense is so strong.

6. Thus: NBC vs. Copiers/Redistributors/Broadcasters, as to the killer's manifesto itself: NBC loses because it has no right to exclude (assuming the killer didn't convey such a right in a signed writing to NBC).

Family vs. NBC: Family loses because NBC has a license from the killer.

Family vs. Copiers/Redistributors/Broadcasters: Family loses because the users are entitled to engage in fair use of the materials.

NBC vs. Copiers/Redistributors/Broadcasters, as to NBC's modest creative additions to the work (editing choices, logo, and the like): NBC loses either because the creative additions are too modest to be protected by copyright, or, even if they are sufficiently creative to be protected by copyright (e.g., the logo), because they are so lacking in detail and such a small part of the copied materials.