"Jungle Queen/Princess" (1977) and "Fast/Quick Draw" have the same thing - 1000 pt doesn't activate the first ball relay, only 10 and 100 pts. But it makes sense on both those machines since you can't hit anything worth 1000 (or 5000) on that machine without hitting something else first or second.
But with "Big Shot", as the OP says, you can make those 2 lanes beside the center lane that give you 1000 pts and then, down the middle. I used to have access to a "Big Shot" - would have been fun to try to see how many times I could do that in a row, getting that first ball over again and again, until I hit something else.