From what i understand from my friends in Lufty they have no restriction on flying visual approaches at night, unlike other german airlines, in my previous one there was a blanket ban on it and we had no problem flying into SFO with that. However, they are not allowed to use visual separation from other traffic at night, which can be done independently of the approach type flown.
To me as an outsider it looks like the type of approach is not the problem, it is the transferring of responsibility in regards to traffic separation from ATC to flight crew which seems to be the issue.