They don't publish which studies they used to get their calculations.
Here is my blog where I compared the elliptical to my HRM and to Spark, you might find it interesting: www.sparkpeople.com/mypage_public_journal_
You are correct that the more info something has, the more reliable its figures. Depending on intensity, I would expect 20 mins on the elliptical to burn between 140 and 180 calories, so both figures seem unlikely.
If accuracy is important to you, especially on this kind of machine, buy and wear a Heart Rate Monitor.