Extreme emotion from people who didn't even know her must be fake, must it not? The evidence is the sea of flowers outside Kensington Palace, and the emetic slogans on home-made banners like "Heaven needs angels too", and the fact that tabloid gossip-columnists who only days before had been slagging her off big-time suddenly came over all grief-stricken.
Not necessarily.
For one thing, as already said by Rhiannon it's undoubtedly true that for some people Diana's death acted as a catalyst for grief of their own, in the way that recently (or not so recently) bereaved people who have been holding themselves together will suddenly break if they drop a glass or something equally trivial. It's the last straw phenomenon.
For another thing, a lot of people were grieved because they saw in Diana somebody who could have made the monarchy (an absurdity in itself, but still) more human, more approachable and more relevant as compared to the ghastly load of inbred, emotionally constipated, hidebound, inarticulate old tossbags that they still are. William and Harry are very much sons of their mother in this.