I have absolutely no special knowledge of this event. All I know I've learned from stories like this. The following caught my eye:
The department also temporarily disabled a technology known as secure sockets layer, used to transmit encrypted information over the Internet.
Hackers can exploit weaknesses in this technology to break into computers, and they can use the same technology to transmit stolen information covertly off a victim's network.
Many diplomats were unable to access their online bank accounts using government computers because most financial institutions require the security technology to be turned on. Cooper said the department has since fixed that problem.
So DoS (heh, pun intended) disabled outbound HTTPS? It sounds to me like the intruders used a HTTPS covert channel (not so covert, actually) to communicate with their victims. I think we are getting to the point where encrypted outbound HTTP will have to terminate on a proxy server that permits inspection or at least logging of the HTTP action. The proxy will then establish its own connection with the remote HTTPS server.
Yes, (1) this breaks end-to-end HTTPS; (2) users will probably have to accept an unexpected SSL certificate; (3) this will undermine any training they may have received to avoid connecting to the uber hacker at https://www.paypa1.com. However, to have any shot at identifying these connections in a timely manner, inspection of clear text at the network perimeter is a must. (What perimeter? It's the line between what you own/control and what you don't.) Not being able to do this probably hurt the DoS.