What exactly are the rules for avoiding the "mixed content" warning in IE due to background images?

This is related to SSL and mixed content due to CSS background images but that question had no accepted answer and the one I'm asking is a little more specific.

Under some circumstances when accessing an HTTPS website, IE will throw the "mixed content" warning if an element is given a style with a background image. I found one forum reference that said the warning can be avoided if you put the reference in a stylesheet, for example

#someElement a {
    width:11px;
    height:11px;
    display:block;
    overflow:hidden;
    background:url(../images/sprites_list.png) no-repeat;
    cursor:hand;
    cursor:pointer;
    background-position:0px -72px;
}

but not if you try to create the element inline, a la

$('#someElement').append("<a title='something' style='background: url(../images/sprites_list.png) no-repeat; ... // etc

and indeed, this works for me. I've seen others that say you have to use an absolute https URL to refer to the image, rather than a relative one.

What is the real story here? Is there some "official" explanation or at least a reference to what the rules are? Or failing that, is there a standard set of guidelines which if followed makes it extremely unlikely to trigger the warning?