One of the most strangely secretive gurus in the world is Gurinder Singh Dhillon, the leader of Radha Soami Satsang Beas (headquarters are in Beas, India).
His predecessor, Charan Singh, had no problem with being photographed in both still shots and videos. However, Gurinder Singh prohibits cameras from being used in his presence, even in public places.
I witnessed this myself when I was serving as a security volunteer at a RSSB meeting in Honolulu, Hawaii.
Prohibitions of that sort, though, can be gotten around. Here's a You Tube video, "Babaji Gurinder Singh Dhillon -- I Just Wanna Hide," that pokes some fun at the guru's secretiveness.
Gurinder Singh also won't allow recordings of his talks, or even, I believe, contemporaneous notes to be taken of what he says. Could be wrong about this, though. I haven't been to a meeting of his for many years.