So I went for a walk, and once I was actively engaging with the world, (I believe) I had some insights.
But first off, the reason I know my friend is an INFJ is because she told me that's what she is. I always pegged her more as an ISFJ, to be honest. Also, I know INFJs aren't exclusively into psychiatry... that's like saying all INTPs are into math, and I have the brain capacity of a small stone when it comes to math! (but I'm good at visual-spatial/music/art)
So, I had this insight of how I would imagine an INFJ director to be. It seems that they would be desiring to construct this vision of either a made-up place or of the future. Chances are, things would be bad. The characters would be more archetype than realistic people. The moralistic hero would either come in and rescue everything or be too late. Regardless, it would be heavy on the moral, which would be something to the extent of, "If we don't change our ways now, this is destined to happen..." Think Avatar.
In other words, yes, I imagine there are a hunk of INFJ directors out there, especially if they are the auteurs and not just adapting someone else's work. I would imagine INTJ's style of film would be pretty similar, except it would be more along the lines of, "If our government continues on this route, or we follow this logic..." well, you know, like Ayn Rand.
XXXP directors, on the other hand, I believe would follow more of a cinema verite sort of line- a snapshot of people's life- emphasis on realistic, believable characters, and the sort of things they have to deal with. If the directors are NPs, chances are there will be some wackiness to go along with it- satirical social commentary, tongue-in-cheek, altered reality; NFPs, chances are it will be somewhat romantic, likely in a tragic, or unrequited sense (Think Before Sunrise or Eternal Sunshine of the Spotless Mind). SFPs will probably focus even more on the verite, things may possibly end sunnier (or they will avoid showing the tragedy), or they will be adapting someone else's work, heavy emphasis on cinematic beauty (or adapting the goofball work of conspiracy theorists... think Da Vinci Code...), or making something like The Hangover, although that could be an ENTP sort of thing... SJs, I can't help but think Westerns and romantic comedies and period flicks.
Obviously I am way generalizing here, so no one get offended. (And please correct me if you consider me wrong.)
Here's the list from TypoC. I'm not saying in any way this is correct, but it's the list they've put together:
Paul Thomas Anderson
George A. Romero
Francis Ford Coppola
Guillermo del Toro
Danny Boyle: xNFP
Ethan Coen: INxP
Micheal Bay: ExTJ
M. Night Shyamalan: INFx
Rob Zombie: xSTP
Tony Scott: ISxP
Howard Hughes: xNTJ
Darren Aronofsky: INxJ
Sam Mendes: IxxP
EDIT: oh, there is someone that I think very much of being an INFJ director and I love... M. Night Shyamalan (I know they have him undecided but he seems very much that way to me.)