how involved was Christopher Doyle with this?

He's credited as the film's "visual consultant", but the actual cinematography credit goes to Andrew Lau and Lai Yiu-fai. Does anyone know to what extent was he involved in this?

I know he was on set at least once, as there's video evidence of it right here:

https://www.youtube.com/watch?v=C22ZJUtH4b0 (10:41)

There's also a part in the video where one of the film's writers refers to him as the film's main cinematographer, and not just a consultant standing by. So I believe he was probably originally gonna be DP for the entire shoot, but then something happened (he probably left to go film 2046 for Wong Kar-wai) which led to Andrew and Lai having to do all the cinematography themselves at a certain point in the shoot.

Is that what happened? Does anyone know?