The "Open" Classroom and Cheating

Question of the Day: Does an "open" assessment approach (open texts, Net, real-time studentsharing) promote or dissuade cheating?

I'm posting this as I'm watching my students take an open Latin assessment. Basically my concern is three-fold:

1) There is no where outside of the traditional classroom that someone would not be able to use whatever resources they wanted to complete a task -- [yeah, yeah, I can already hear the desert island iPhone battery jokes]. 

2) What we usually call "tests" are anything but.

3) As far as "cheating" goes: why not just create assessments that a) don't assess the ability to memorize and b) are different for each kid?

Want to know your thoughts. Do you give open assessments? Do you let students use resources (Net, notes, each other)? How do you define "cheating"? Why do teachers create assessments that can be "cheated" on?