My understanding is that there would be no insurance payouts, including to the owner of the WTC, if there was an "official" declaration. By "official", I mean with by using the title "Declaration of War". However, the wording in the Joint Resolution is not my any means vague. It is clear that Congress FULLY authorized the use of Military Force, and that the State of War already existed at the time of the Resolution.
This is all the more reason to declare war. Congress is abusing its power to hold insurance companies responsible for "acts of war" which their policy specifically excludes. In effect, insurance companies are being robbed by Congress.
The wording in the Joint Resolution is "vague" in that it did not clearly state that Congress was "declaring war" when it could so easily have done so. None of the arguments I have seen on this thread (e.g., insurance clauses, identification of an enemy nation, etc.) are persuasive justifications for Congress' failure to "declare war".
But as I stated in my previous post, the issue isn't quite as clear-cut as I once thought it was. The Constitution does not prescribe the exact format of a Declaration of War (nor does it require a 2/3 vote to declare war as FreeTally argued). Different wordings in different resolutions have been employed in the past to declare war, so one can at least plausibly argue (whether or not the argument is ultimately validated) that this Joint Resolution Authorizing the Use of Force Against Terrorists fulfills the essence of the Constitutional requirement. But the counter-argument is at least as plausible.
Because Congress failed to clarify the matter, we are not going to be able to avoid these neverending disputes about whether our military actions were properly authorized. The President could also have asked Congress for a Declaration of War, but that is only advisory; the Constitution places the responsibility solely on Congress. And therefore I place the blame on Congress for another screw-up.