I'm not saying I think it shows good moral character for someone who knows the rules to be doing what Henning did (and as a Student Pilot at the time, one would not expect him to know those rules), but for someone other than an ATP (which IIRC Henning is not anyway)...
The PIC might be violating 135.115 regarding manipulation of the controls, but I don't see how a passenger not assigned as a crewmember would be violating 135.293 regarding pilot testing requirements by touching the controls with the PIC's permission (that permission being necessary to avoid a 135.120 "interfering" violation on the passenger's part).
As for 61.59, I'm not seeing any falsification there, either -- Henning really was receiving training from that instructor in that aircraft. I don't see how the fact that Part 135 was being violated by that instructor affects the legality of Henning's logging of the time IAW 61.51 on pilot logbooks. Would a Student Pilot be violating 61.59 if s/he logged the time while flying solo with less than 3 miles visibility? Yes, the 61.87 limitations on Student Pilots were violated, and probably 61.155 regarding VFR flight weather mins, too, but there was no falsification involved -- s/he really did fly that time, just as Henning really did receive that training from an authorized instructor, even if some Part 135 rules (but no Part 61 rules) were being violated by that instructor in doing so.
So maybe that's why the DPE who saw his logbook just chuckled and moved on.