To my knowledge this is incorrect. Assistive technologies don't recognize input names when nested inside of label elements, and as a result is frowned upon by the W3C. Unless you meant something else by, "...HTML has always allowed nesting an <input> inside <label>..."
The results on that page puzzle me for the nested input/label case - this is news to me. Given how browsers already forward focus for clicks on a label to the nested input, I always assumed that this takes care of programmatic association between label and input.
Maybe an aria-labelledby attribute would fix this? Heck, could still use a label "for" attribute and keep the input nested.
Either way, I meant that it is legal HTML to do that kind of nesting. Did not know that it was frowned upon, as far as standards are concerned, even assistive.
Source: http://www.w3.org/TR/WCAG20-TECHS/F68.html