document.ontouchmove and scrolling on iOS 5

Update Per Alvaro's comment, this solution may no longer work as of iOS 11.3.

You should be able to allow scrolling by selecting whether or not preventDefault is called. E.g.,

document.ontouchmove = function(e) {
    var target = e.currentTarget;
    while(target) {
        if(checkIfElementShouldScroll(target))
            return;
        target = target.parentNode;
    }

    e.preventDefault();
};

Alternatively, this may work by preventing the event from reaching the document level.

elementYouWantToScroll.ontouchmove = function(e) {
    e.stopPropagation();
};

Edit For anyone reading later, the alternate answer does work and is way easier.

The only issue with Brian Nickel's answer is that (as user1012566 mentioned) stopPropagation doesn't prevent bubbling when you hit your scrollable's boundaries. You can prevent this with the following:

elem.addEventListener('touchstart', function(event){
    this.allowUp = (this.scrollTop > 0);
    this.allowDown = (this.scrollTop < this.scrollHeight - this.clientHeight);
    this.prevTop = null; 
    this.prevBot = null;
    this.lastY = event.pageY;
});

elem.addEventListener('touchmove', function(event){
    var up = (event.pageY > this.lastY), 
        down = !up;

    this.lastY = event.pageY;

    if ((up && this.allowUp) || (down && this.allowDown)) 
        event.stopPropagation();
    else 
        event.preventDefault();
});