Neighbor unclear on the concept

So I hear Murphy out on the deck just barking away. And it's not his "I see a cat" bark, or his "There's the UPS truck bark". No, it's his serious "I will kill you" bark. Naturally this one gets my attention quick so I go out on the deck where he is only to see him with his head between the deck rails with his ears pinned back and his hair up, straining with all he's got to reach one of my cat-harboring neighbors, who is in my yard trying to recover one of the feral cats that she's got a thing for. She's about 6-8 feet from the deck rail and she's actually trying to reach up and offer her hand to Murphy despite the fact that Murphy is clearly promising all sorts of pain and scarring if he gets hold of it.

"Aw, come on," she's crooning. "You know me..."

"Yes, he does know you," I replied. "And he doesn't care. You're in his yard."

I get Murphy back and bring him in the house, rewarding him with a cookie because he did the right thing even though the target was ostensibly friendly. Then I went back out to clue her in.

"He sees me in my yard every day," she said. "He's normally nice."

I sigh. "He knows that you belong on the other side of the hedge. He may be fine with you over there or out on the street, but this is his yard and he's going to defend it from anyone, you, the UPS guy, the meter man..anyone. It's what he does."

"Well I just figured I'd let him smell my hand and he'd remember me," she said.

"And that would be fine in your yard or down on the street," I reiterated. But if you reach up into his deck in his yard, he's going to bite you."

"Oh, I can't believe that he'd do that," she replied. "That's just crazy."

I sigh again, thinking to myself that Murphy's not the crazy one here. Every facet of his tone and body language promised carnage, but she's convinced herself that she "knows dogs" and can pet him.

Good job on the defense, Murphy, but don't bite the crazy lady and get us sued, ok?

"I will give you dis beer if you look the other way next time she comes back."