This is, and I believe will continue to be, a much different response than those initiated by Abdalihi al-Shayea's claim that al-Qaeda was not involved. The landscape of the debate is now changing and the ground is being softened for a future AQAP statement either supporting the executions and kidnappings or taking credit for them. AQAP can now present itself as a defender of Islam in the heart of the Arabian Peninsula instead of as a group of grisly murderers.
AQAP is involved in constant battle for popular support in Saudi Arabia and Yemen and these tragic events give it yet more leverage - once again it can tell its audience that the Yemeni government is in a secret alliance with "Zionists and Crusaders" to undermine and destroy Islam. The government, it will argue, let these agents into the country under the guise of helping the people of Yemen but really they were only here to turn our brothers and sisters away from Islam.
This is a powerful argument in Yemen and will resonate with many, even those who aren't members of al-Qaeda or don't offer overt assistance to the organization.
(Note: I'm not saying that I agree with this argument, only that it is one that AQAP could make quite easily, which would be yet another propaganda coup for the organization, presenting itself as the one true defender of Islam - I don't think I need to explain that to most people who read this blog, but one never knows who stumbles on to Waq al-waq through some Google search.)