Funny you should mention this as this point is the only reason I would NOT add my name to DP credit. And by the way, there were no light readings, no flags set up, no light planning without my plans << note - to be fair, the director is usually involved in this process during pre-production with the dp/gaffer working out the technical necessities to achieve the director's vision -- d >> , no kelvin ratings (in fact he had the wrong white balance set on his B-cam for the first 3 days of shooting). No composition, planning, location scouting...
Some of his B-cam stuff was great though and really saved my butt sometimes in the cut. Being honest he was a B-cam operator, a best boy and key grip (an gave rigs and B-cam to the shoot). There were a couple of occasions when he set the room up with nice soft lighting but not very often. I guess because the shoot was on the fly I just knew what i wanted from each shot so he perhaps never really got time to have an input on composition.
(Bold emphasis mine, <<comments in brackets>>)
TBH:
It sounds like you didn't have a director of photography at all. It sounds like your production workflow was such that you operated a camera, another person operated a camera, and - as director - you just bypassed having a cinematographer on set as a dedicated job function.
Frankly, no one should get a "director of photography" credit. At best you can pull a Shane Carruth and give yourself an operator credit along with a "cinematography by" credit as well. (see full credit listing for UC and probably Primer, iirc) Because let's be honest with each other - no one on your set was functioning as a director of photography or as a cinematographer. Creatively, you were acting as the director of the film - but practically (for whatever reason, choice, lack of resources, whatever, doesn't matter) you had to function as a camera operator, with a b camera operator by your side. "Director of Photography" is a job title though, and since no one was really doing that job (your creative leadership of the lighting, composition, etc in this instance falls under the auspices of your role as director) there's no point in using that specific credit at all.
It's just a different style of working, and if it works for you, then keep doing it and stop worrying so much about the various job titles.
Edit - I don't mean to imply that just because someone successful is doing something that you should mimic it, simply to state - by way of example - that there are alternative ways to dole out credit for work besides just using traditional titles where they don't necessarily fit.