“White House Communications Director John Kelley....”
Nonetheless, it is worth investigating. For that matter, how hard would it be to jam anything coming into or going out of that house? Then it doesn’t matter what they have, they can’t send or receive it.
More likely, the leaks come from people who are disloyal at least to Trump, and more likely to the nation as a whole (especially when ANYTHING classified is leaked). These folks are reasonably easy to smoke out, you just need someone (preferably retired) who knows a bit about spycraft and, in particular, in counter-intelligence. Most of the leakers are political types, and an intelligence vet will be able to run rings around these people.
"White House Communications Director" should be "White House Chief of Staff", or:
"White House Communications Director.." "White House Chief of Staff.."