If something bad happens during the flight the FAA will consider Pilot
#2 PIC. Pilot #1 can not act as PIC without a current BFR. So if pilot
#2 is taking the responsiblity he might as well log it.

My somewhat simplfied interpretation of the FARS for PIC is as follows.

1. A pilot may only log PIC only if they are legally qualified to fly
the airplane as the solo, Note 90 day currency must be met if any
passengers are on board. (note there may be a few exceptions)

2. Both a Pilot and Safty pilot my log PIC when performing simlulated
instrument flight. Both must meet #1.

3. A Flight instructors may log PIC when giving instruction to pilots
that meet #1. But should be careful not to abuse this. i.e. does the
pilot really need instruction for insurance, currency, ratings, etc.

There are some other possibilities, for logging PIC but the above are
the basics according to Brian.

Brian
CFIIG/ASEL