I'm interested that he called out the idea of "deep state." He defines it as political forces that outlast a presidency (by that definition of course it exists i.e. any political party), but perhaps the implied element is a secretive nature and power over a president.
I wonder if there's an objective way to answer this.
FBI director J. Edgar Hoover was example of single man holding some amount of 'deep state' power.
There justified is fear that increased secrecy in security apparatus in US has started acting in more autonomous way. In the current government the power over WH likely comes mostly from competence difference.
Instead of seeing this as some sort of covert manipulation, maybe this phenomenon is a reflection of just how much people prefer the status quo. IIRC a lot of jurisprudence is based on deferring to status quo. It seems natural that a new president's administration should remind them "hey, listen, we've thought about item Q on your agenda a lot and we can't do it because of X, Y, and Z."
On the other hand, I've shown up on software teams before and asked, "Hey can we try Best Practice X?" -- only to learn that "Yes, we have all thought long and hard about Best Practice X but it Just Couldn't Possibly Apply Here. Also, Dave doesn't care for it." ;)
Annie Hacker: No of course not, silly of me. They're just called the opposition.
James Hacker: They're only the opposition in exile. The Civil Service is the opposition in residence."
Curiously, this dialogue appears in an episode called Big Brother, in which the Minister is trying to add safeguards to a national citizens database.