My current job (as noted here and here) requires me to spend a lot of time researching doctrine documents to derive space requirements. One such document is Joint Publication 1-02, "Dictionary of Military and Related Terms", which defines "preemptive attack" as follows:

"An attack initiated on the basis of incontrovertible evidence that an enemy attack is imminent."

(Emphasis added)

Back to your example of neighbors living in a remote area. If one neighbor sees the other coming his way with a gun in his hand and blood in his eyes, he'd be an idiot to just sit there waiting for the other guy to get off the first shot. That first shot might prove fatal.

The same applies to nations, as demonstrated by Israel at the start of the "6 Day War" back in 1967. Israel had incontrovertible evidence they were going to be attacked, so the IAF was ordered to hit first. They did, and in about an hour they took out some 300 of Egypt's 340 combat ready aircraft.

By that definition, Japan's attack on Pearl Harbor wasn't a preemptive attack because there was no indication that we were going to attack them. Instead, the attack fit into Japan's military doctrine at the time of striking a decisive blow against the enemy to force him to accept terms. They hoped to cripple our Pacific Fleet and force us to accept their terms. They looked at our opposition to getting involved in the European war as a sign of weakness and believed we didn't have the will to fight. Yamamoto, who had spent considerable time in America as a Naval Attache, was under no such delusion. Following the attack and upon learning that Japan had hit without first delivering a declaration of war, "I fear we have woken a sleeping giant."

9-11 appeared to wake us for a time but a lot of people appear to be drifting back to their slumber. Will we need another wake up call before they take the world seriously?