Wrong, they can both log PIC. The safety pilot can log PIC if he also
serves as PIC because the FAA says safey piloting is an operation which
requires multiple crew members read 61.51(e). The flying pilot logs PIC
because he is on the controls. Please understand that LOGGING PIC is
***DIFFERENT** than SERVING as PIC.
You need to read some of the FAA pubs, including the Lych FAQ.

-Robert, CFI