Stonewall,
Your line of thinking is fairly close to mine on the issue. However, even if the deck is often stacked against the landowner that doesnt change the fact that people often do not have the legal right to shoot dogs even when they think that they do.
As an added complication, the person who started this thread is leasing the ground. Dunno if leasers have the same rights as landowners in this situation across states. Furthermore, and this is a big if, if the landowner has less of a problem with dogs on the property than the leaser and doesnt agree with shooting them (legally or illegally), it is a good way to lose the lease. The issue is often much less clearcut than people think.