No, not rude at all and not wrong. Its up to you to decide who you do and and don't want on your friend list. If she pushes the issue, tell her that you prefer to keep your friend list to only those you are very close with, family, etc. That's how I use FB, and everyone uses it in a different way. Some use it to play games, and have lots of friends realting to said games, others, like myself, use it to keep in touch with family and friends.
And just as an aside, I don't feel guilty or think its rude when I do certain other things on FB. A lot of my friends play games, or send me stuff, and every time I get a notification that someone wants me to join something, or sent me something and wants it back, I block each and every application. I don't tell anyone, and no one has said anything. If they did, I;d simply tell the truth, I don't trust any games or apps on FB, as my computer is a bit fragile, and I also know people who have gotten viruses from FB apps, and killed their computer completely.