Is that definitely the case? Chrome, Firefox, and Safari all return a value for the innerHTML property of an element in an SVG document.
This W3C spec [0] specifically mentions XML documents in addition to HTML documents. And as I understand it, it seems like embedded SVG elements also inherit from the Element interface which includes InnerHTML.
IE11 might also be correct, following an older spec, but I don't think you can jump to the conclusion that Chrome is wrong just because the property is called innerHTML.