I'm still receiving totally contradictory info about ADAC recovery - some saying that an ADAC truck accepted their card and others saying it was refused. The position appears to be rather random at present ...

The cost of recovery from the on-site trucks is €185. Note that this is very much cheaper than trying to limp round with a broken car: see this page.

The standard recovery fee only gets you back to the car-park - if you want to be recovered on anywhere else, you are strongly advised to agree the additional cost in advance, as the rates can be high. It is usually best to arrange your own onward-recovery once off the track.