A Sign of the Times

I saw a sign in a yard today. It read "Trespassers will be shot on site." Perhaps this is one of the negative consequences of the Internet. People mix up the word site with sight. Or, perhaps the sign says what the owner means. I always assumed that the phrase meant that, if seen, a trespasser will be shot. If this were the meaning it ought to read "Trespassers will be shot on sight." That is to say that when a trespasser is seen, they will be shot. As written, the sign I saw today informs me that anyone trespassing will be shot there on the grounds where their offense has taken place. They will not be shipped off to another location in order to be shot. May I suggest that the most accurate version of this warning might be "Trespassers will be shot on sight, on site."
Correct me if I am wrong.