[SalesForce] Cannot disable locker service for recently created Sandbox – Summer 16′

This is because you are trying to access the DOM elements in the init handler before they have been rendered. Even if you use the native document.getElementById('myDiv') call inside the init handler with LockerService disabled, you'll get null back.

If you move your find('myDiv') call to a button click handler it will return the correct SecureComponent object.

Also, the access="global" on a div element won't do anything useful. That property is specifically for Aura types (components, attributes, etc).

Edit (Nov. 16):

From Doug's comment, for situations similar to this you may want to explore custom renderers. Handle with care though.

https://developer.salesforce.com/docs/atlas.en-us.lightning.meta/lightning/js_renderers.htm?search_text=renderer

This isn't related to LockerService: it's due to the difference between DOM (object) and HTML (string).

There seems to be 2 errors in the code:

component.set('v.html', button.innerHTML)

1. Using innerHTML inserts the content, not the <div> itself on which the handler is attached.

2. Using innerHTML converts your DOM elements to an HTML string and JavaScript handlers are lost.

Solution: if you create objects (DOM nodes + JS function), you can't convert them back to HTML.

This example app and controller does work:

<aura:application >
    <aura:attribute name="html" type="Object"/>
    <ui:button label="start" press="{!c.press}"/>
    <div aura:id="container"/>
</aura:application>


({
    press : function(component, event, helper) {

        var button = document.createElement('div');
        button.appendChild(document.createTextNode("test"));
        button.addEventListener('click', function (e) {
            alert(window+'');                 
        });
        component.find("container").getElement().appendChild(button);
    }
})

With LockerService "on" (v40+), you get an alert showing "SecureWindow" as expected.

There are many other ways to insert DOM in components. You can look at afterRender() if you want to do it on init.