Try hitting a key. Then try adding a hash to the omnibox. TADA!
<script>
var down = false;
document.addEventListener('keydown', function (){
    down = true;
}, false);

document.addEventListener('keyup', function (){
    if(down === true){
        alert('It was from the page!');
    }
    else{
        alert('Omnibox. Ignore it.');
    }
    down = false;
}, false);

</script>