Beardy .. I still think you are completely wrong, CDS had a DUTY to speak out IMHO. Try looking at it this way, a tad extreme but hopefully makes the point ...
A political leader makes the decision to deploy British troops to a war zone - that is a political decision that CDS must obey - however, if that politician then publicly announces that those same troops cannot take any ammunition with them in case they are tempted to use their weapons, then he is putting the troops in "harms way" by limiting the military use of the weapons provided and I would expect CDS to speak out to protect his troops.
The political decision to own nuclear weapons has been made, and until that decision is reversed - which I agree is outside the remit of CDS - then the statement that they will not be used potentially puts UK PLC in harms way, and CDS is right to speak about the matter when asked.