It turns out that you can set window.undefined to whatever you want, and so get object.x !== undefined when object.x is the real undefined. In my case I inadvertently set undefined to null.

The easiest way to see this happen is:

window.undefined = null;
alert(window.xyzw === undefined); // shows false

Of course, this is not likely to happen. In my case the bug was a little more subtle, and was equivalent to the following scenario.

var n = window.someName; // someName expected to be set but is actually undefined
window[n]=null; // I thought I was clearing the old value but was actually changing window.undefined to null
alert(window.xyzw === undefined); // shows false