Actually no, it's not live right now. I had to take it down to do some major changes. But when I try the same thing on your demo, I get the same result. Also, if I click on table properties instead of the cell/row/column, I get a grayed out box on those properties...can't edit that whatsoever. I will attach a screenshot of me on your demo site to this and in my next post a shot of the grayed table properties boxes.
One other note about your demo site, the little white box with the disclaimer about "not being able to save changes in demo mode"...on my pc ( vista ultimate 32 bit , IE8 6.01)..the wite box is not showing up...just the text...you can see that also on both the screenshots..