Does anyone know what the rules are around logging total time?

My specific example is a person who flew literally hundreds of hours
before getting a license (no solo privs either). He performed all the
duties of the flight including take-off, cross country navigation,
landing, communications, maneuvers, etc... He was always accompanied
by someone who was acting as pilot in command, but whom never touched
the stick. Is it legal for him to log total time for these flights?
Is there a way to log total time without logging either PIC, SIC, or
Dual Received/Given?

Thanks for any responses to this.

z