Re: Wrong
"a reddish-black dye"
Yes what you mention is correct, but Osama's beard is dark black. It is not henna or katam dye which have a red tinge or mouse grey.
Check it...
http://www.mehandi.com/shop/buxus/index.html
His beard in the video looks very black, right?
"Changing grey hair by dyeing it black is haraam. This is the opinion of the majority of scholars, who forbid it completely, because of the hadeeth of the Messenger (peace and blessings of Allaah be upon him), when he saw Abu Quhaafah. Jaabir said: the Messenger of Allaah (peace and blessings of Allaah be upon him_ said, when he saw his head looking as white as the thaghaamah plant, “Change this…” (Narrated by Muslim, 2102)."
"...What is prohibited is making the hair pure black, but if something else is added to henna, such as katam etc., there is nothing wrong with that. Katam and henna make the hair a colour between red and black, unlike wasmah (woad leaves) which make the hair black as coal. This is saheeh. (Zaad al-Ma’aad, 4/336)."