That's clearly not true. Two private pilots can log PIC at the same
time. Pilot #1 is sole manipulator of the controls (61.51(e)(i). Pilot
#2 is a required crew member serving as PIC 61.51(e)(iii).

Reference. FAA 61 FAQ...
ANSWER: Ref. § 61.113(a) and § 61.51(e)(iii); Yes, the Private Pilot
who is serving as a safety pilot and is acting as the PIC may log the
time as PIC flight time. And yes, that Private Pilot may use that PIC
flight time for the furtherance of a pilot certificate and rating under
Part 61. And no, that Private Pilot is not ". . . . carrying
passengers or property for compensation or hire;" nor is that Private
Pilot acting as a pilot in command ". . . for compensation or hire, .
.. . ." when he serves as a safety pilot. In accordance with
§91.109(b)(1), it permits a person who holds a Private Pilot
Certificate with a category and class rating appropriate to the
aircraft being flown to serve as a safety pilot.

And this answer has been reviewed by the FAA's Washington HQ Chief
Counsel Office (AGC-240), and they have agreed with this answer.
{Q&A-273}