The fact that it's a recipe from a book, makes her rude for not sharing. If it were truly HER OWN recipe, then I would understand wanting to keep it secret.
But why does this make her rude? I agree that for me, it does make a difference if I have a recipe of my own, or out of a book. I am more likely to share a recipe anyone can find.
But, there is also a recipe that *I* make in my circle, and that I want to be the only one to make. I found the recipe, have perfected it and make it often. I don't think it's rude not to share it.
Perhaps not rude, but decidedly unfriendly because but for that little bit of information, that many people must stumble upon unknowingly on a daily basis, the OP could have cupcakes of her very own. By holding on to that information which is not proprietary
(the name of the cook or the cookbook) the friend is...well, is being stingy.
And I honestly don't see why people get so fussed about actual proprietary recipes either. Every time someone makes something, there will be differences, due to different stoves, different ingredients, carelessness and accidents in measuring, or the tweaks that cooks give to their baking. I've been making "my mother's" spaghetti sauce for years now, and I still
like her's better!
In fact, there's a dozen ways to make it a sharing and teaching experience, from "here's this recipe and here's why it turns out so nice," to "come over and let me show you how to do it, we'll do it together the first time." Frankly, the fact that she doesn't want to share strikes me very much as saying "I don't really like you as much as you think I do."