I don't think there is a right or wrong here. I just know that I'd probably do what your buddy says he would do. That's just my nature.
DD anyone? No not Dungeons and Dragons.
This is the correct response. I have used similar responses before three or four times, it's good fun, if you make her laugh, you feel great even if she never calls. It shows her you can take rejection (if she is rejecting you) and it shows her that you're funny and interesting (if she is on the fence, or really doesn't make a habit of giving out her number to complete strangers she met five minutes ago).
I would take my chances and give her my number. Because as you say, she might call. By giving her your number you have nothing to lose and everything to gain.
Wait twenty years.
You'll look back laughing you even had such things to argue about.