A “defamatory statement” is any statement that an ordinary person would find damaging to their reputation and character. If you're OC'ing, it would be hard to argue stating you considered stating you had a firearm is damaging to your reputation. Saying you do not have a permit... well, that may hurt your rep on opencarry.org, but doubt most people consider that damaging to your rep or character.
Intentionally lying about that to the dispatcher in saying you didn't have a permit... they could go after him for a false report, but that's completely up to them, and in this case it would probably be hard to show clear intent, since he answered honestly on everything else, and would simply say that's what he thought you said (Which is actually rather easy in this case, as human nature tends to hear "it's not needed" as "No, because it's not needed). I don't see how you could claim any actual damages, so any civil action would be pointless.
W/O knowing the department procedures, my assumption would be 9 cars would have needed dispatch instructions to go there. Those out on patrol usually don't have a set path, and sometimes pass by or near other calls, or head there if they aren't on another dispatched call. (I have heard on the scanner officers reporting to dispatch that they will also respond, and that being acknowledged by dispatch) but I think typical stay within designated sectors or areas to ensure broad coverage of the jurisdiction, unless they are specifically dispatched. So I'm guessing the dispatcher probably directed multiple to the area. A lot of that may just depend on how slow the night is going for them. If there aren't any other calls needing attention, why not be a little over prepared?