Disagree - having written a bunch of these gist extractors I have found that the good ones do not produce out of context paragraphs. In fact, that's pretty much the point - to find the salient portion of the content.
They are out of context because they (we) are basically just doing extraction. In which we just extract the most important sentences, arrange them in order, and present it in a paragraph / list. I prefer presenting the top sentences in a list though. In my opinion, presenting it as a paragraph will make an effect that it's out of context rather than in a list.
If the summaries was done through abstraction, like how humans are doing it, it will obviously produce better summaries. But why we are not doing it? I believe abstraction summaries are holy grail of automatic summarization.
You should have a few links listed on that page that you know will work well as examples for people to try the service out with.
Btw, how do you feel about my other comments in this thread about algorithms not working well? My basic point is that they will most likely produce paragraphs that are out of context.