Javascript function gets incorrect boolean value from controller

When the page loads, the {!myBoolean} expression gets the value of myBoolean at the time of the page load. So essentially the javascript function in your page would be:

function myFunction(){
   window.alert(false);
}

If the value of myBoolean is changed in the controller, you would also have to rerender the javascript function, or else it would remain as alert(false);

Moving the javascript function inside the something block should solve your problem.