Islamic Greeting For A Wrong Number

There was a man named Mohammed who had the phone number I have now.

From time to time, we'll get phone calls for him.

Lately, a woman has been calling us. I'm not sure if she is calling for him, or just dialing for someone with a similar number to ours.

Whenever she calls, since hers is a voice I don't recognize, I automatically just say, "You have the wrong number." I haven't understood what she is saying -- she was not asking for a person's name.

Tonight, however, I think I understood.

She was saying, As-Salāmu `Alaykum. A common translation of this phrase is, "Peace be upon you." Now, if I answered the phone, and the first thing someone said to me in English was "Peace be upon you," I don't know that I would so abruptly say they had the wrong number. I'd be kind of thrown off a bit. In my mind, that's a powerful and loving thing to say to someone, especially a stranger.

According to the Wikipedia article I link to above:

"The traditional response is "wa `Alaykum As-Salām", meaning "and on you be peace."

Should I practice the pronunciation of this response?

I don't know... I found a website, How to Greet Non-Muslims? which says that "As-Salāmu `Alaykum" should not be used as a greeting for non-Muslims. Is this website definitive? Is the exchange of these greetings between a Muslim and a non-Muslim seen as an egregious affront to Islam by a large group of Muslims? A small group of Muslims? Any?

Can I wish peace upon someone who wishes peace onto me?

What do I say?

Wrong number?