But if a pilot wants, they may allow any person to handle
the controls, but then neither may log that time.

As I understand it, the person ACTING as Pilot In Command may always log the
time (as total time and PIC time), whether that person is sole manipulator
of the flight controls or not. More than one person can certainly log PIC
time, but I can't think of a circumstance when nobody can log PIC time.

-Mike