Unfortunately, that's not entirely correct. An instructor giving instruction may also log PIC time without being either the sole manipulator or the PIC. Likewise, an ATP commanding a flight requiring an ATP may log PIC time regardless of who's flying or how many pilots are required.
Since not many single-pilot airplanes are used in operations where only one pilot is required, this is pretty much true. However, there are flight operations which by regulation require two pilots even if the aircraft requires only one, mostly under Part 135. In these cases, the PIC may log PIC time when the 135-required co-pilot is flying the aircraft, even if the aircraft itself requires only one pilot.