Here's what the Campaign for Nuclear Disarmament have to say about how the disarmament symbol has been used abroad and in other contexts:

"The Disarmament Symbol goes global
This "CND logo" was not however confined to these shores. The "peace symbol", as it is usually dubbed outside Britain, was first brought over to the United States by Bayard Rustin, a key figure in the civil rights movement of the 1960s and a protestor at the 1958 Aldermaston march. Consequently, the symbol was used in civil rights marches and later spread to anti-Vietnam War demonstrations. Since then it has appeared around the world not only as a sign for nuclear disarmament but also as the international hallmark of peace." [...]
"The Freedom of the Peace Symbol
[example of an advert using CND symbol was here]
Although specifically designed for the anti-nuclear movement it has quite deliberately never been copyrighted. No one has to pay or to seek permission before they use it. A symbol of freedom, it is free for all. This of course sometimes leads to its use, or misuse, in circumstances that CND and the peace movement find distasteful. It is also often exploited for commercial, advertising or general fashion purposes. We can't stop this happening and have no intention of copyrighting it. All we can do is to ask commercial users if they would like to make a donation. Any money received is used for CND's peace education and information work."

In response to a message below, I find it dissapointing somewhat that the CND logo has been diluted to more general terms. I find it dissapointing as I clearly remember when growing up in the Eighties the stand that the women at Greenham Common made against Cruise Missiles being stationed there (I believe this camp was the longest lasting in the world). The CND logo really meant something very specific in campaign terms, and people made vast efforts in campaigning against nukes (Greenham Common Peace Camp), it really wasn't just a token general 'symbol' and it still does mean something very strident to me.

I thought it interesting however that CND have chosen not to copywrite their logo, and have intentionally left it to be used by anyone who wishes to.
SO at the end of the day, I guess the choice was made by CND themselves to freely allow the disarmament logo to be used outside of their specific nuclear disarmament agenda.