[rolling_stone]

methinks you are wrong
unsounded is different than unaccented.

http://owl.english.purdue.edu/owl/resource/591/01/

[Verginius Rufus]

That just begs the question--when is the "h" unsounded?

I'm not going to take something from Purdue as definitive. They won the Rose Bowl only once, and that was back in 1967.

It may be that pronouncing an unaccented "h" is more common in America than in the UK. I have a book which has a title starting An Historical Commentary... (published in England, but the author was a Canadian, or at least was living in Canada when he published the volume).

My preference would be to let each person do as he or she chooses on the matter. Hopefully Sebelius won't issue a mandate ordering one or the other.