Glad someone other than me has raised this point, which is one of my pet
hates.
The term that "the grown-ups" used in my childhood was "watery
sunshine", or "a milky sky", and I have used it ever since when talking
non-technically. It would be acceptable for presenters to use. As you say,
Jack, it is most definitely not haze, which reduces visibility and gives a
brownish-yellow tinge to everything. The persistent misuse of the term over
the last 10 years or so now means that many members of the public have lost the
distinction as well, or are confused. This probably wouldn't have happened if
we still had fully-fledged meteorologists doing the presentation, but many of
the present lot, especially the female ones, have little feeling for the
weather. I feel it's time to gently educate the public rather than pander to
their (often wrongly)-assumed ignorance.

Best wishes, Tudor Hughes, Warlingham, Surrey.