My english is pretty bad. What I mean is that even if your math are right (didn't check), a less than 1% possibility doesn't make an event unlikely. Like getting a royal flush on a single hand is almost impossible since it's less than 1% chance but it should still happens often on the long run. I don't say nothing is wrong with JD but what is happening is far from impossible so we can't be sure something is wrong.
I understand what you are meaning and it is called selection bias in statistics, but you are misapplying the concept. You are correct that if you play 2 million hands and only select the one hand you actually hit your royal flush to prove a point you are making a big mistake.
Same would be if there were 100 different sites just like just-dice and I picked only the one that was most unlucky to prove something bad was going on I would be making a big mistake. However I am using the full (and only) sample we have so I am really not cherry picking anything.
Here is another example where I would make a selection bias mistake. Look at the betting streak in this post:
https://bitcointalksearch.org/topic/m.3263667He hits 31/38 bets. Now I could say the odds of that happening is like 1/35000 so he has to be cheating. But no, that is a mistake because that sample has been picked out of a much larger sample just because he was extremely lucky in that streak. Because of this I would need to adjust those odds a lot if I was going to try to use that streak to prove any kind of point.
Hope I have explained the difference for you.
I can recommend the following book if you are interested in selection bias and how to adjust for it in real life situations:
http://www.amazon.com/Evidence-Based-Technical-Analysis-Scientific-Statistical/dp/0470008741/