You can turn it off, but you have to go into a menu to do it. You can't assign OIS on or off to one of the 3 user assignable buttons. It takes about 30 seconds to switch anything back and forth, because of the nested menu system, about 10 clicks of various buttons to do it.

On my Sony HC1, which also doesn't have a lot of buttons, they had a neat system called, personal menu, which was the 'top level' most important menu items that you'd see at the 1st level of entering the menu system and you could assign anything to that 'personal menu'. It was a way to mitigate the fact that you had a limited number of buttons but you could fairly quickly get your setting. I wish JVC had at least something like that.