"Most people" in this case includes the FAA Chief Counsel.
FAA Legal-Safety Pilot may not log XC
"As discussed above, the safety pilot is a required flight crewmember for only a portion of the
flight. Section 61.65(d) contemplates that only the pilot conducting the entire flight,
including takeoff, landing, and en route flight, as a required flight crewmember may log
cross-country flight time. Because a safety pilot does not conduct the entire flight, a person
acting as a safety pilot for a portion of the flight may not log any cross-country flight time
for the flight. In your example, Pilot A may log the entire flight (2.2 hours) of cross-country
flight time because that pilot conducted the entire flight. However, Pilot B may not log any
cross-country flight time because that pilot was a required flight crewmember for only a
portion of the flight."
The safety pilot did not do a takeoff and landing. If the pilots switched flying pilot and did their own takeoffs and landings, then it would seem to meet the requirements. Each pilot would have been a required crewmember during each phase of flight. Of course during each T/O/L, one pilot is not required and cannot log that time.