Director of gubbins
The role of the directors is twofold.
First, to have a plan for the future of the business (which could include fixing any existing problems) and to be able to communicate that plan to the senior managers who's job it is to execute the plan. Directors aren't the "do-ers", they express a wish and others are resonsible for carrying it out. If you ever see a director of IT doing a technical job, something has gone terribly wrong.
Second, to be responsible both to the shareholders and the law for the operations of the company. As it turns out, large companies have many IT related legal obligations (security and protection of data being just one). However, it's not the job of an IT director to specify the "how" - that's too low-level - they specify the "what" and leave the "how" up to the minions, but with final say over all and any proposed solutions.
As such, it makes complete sense for an IT director to be only partially IT-savvy. Just as you don't expect a Network Manager to know about the header fields in an Ethernet packet. An IT director needs to work at the "block" level of infrastructure: a computer centre here, a D.R. site there. And to be aware of which directions the industry is moving in, in order to increase the IT value to the company: do we stick with our own operations, or do we outsource? do we put everything in the cloud?
However, since practically everything in a commercial organisation is money-driven, it's not unreasonable for an IT director to be better at doing spreadsheets than installing Linux.