But let's not lose sight of what a LinkedIn connection also entails: it means that all of your other connections are now visible to each other, and to some people that may imply a degree of exclusivity. To some, LinkedIn is not a contact-free-for-all like Facebook, where one can be "friended" casually.
A LinkedIn connection isn't like walking into a business and cold-calling on an owner or manager. It's the equivalent of walking in and demanding to see their address book of contacts.
Others in this thread have indicated that the best response would have been to ignore the request. I agree. But some people don't work like that, which is why I referenced a truncated response perhaps would have been ok.
Yes, the response was rude and insensitive....and so is the entire world outside of the comfy confines of white-collar America. The requestor made certain assumptions she should not have, and her follow-up approach to the situation seems to imply a sense of entitlement.