Panam,
A safety pilot may log cross country time, if the time has been accordance with the various provisions of FAR 61.1(b)(3) for which the time is being logged. Specifically, for generally logging a cross country flight as cross country, there is no requirement under 61.1(b)(3)(i) for the person logging the time to be pilot in command, or sole manipulator.
A safety pilot is a required crewmember in accordance with 14 CFR 91.109(b)(1), and may log night time, instrument time, and cross country time even if not acting as PIC, or sole manipulator of the controls.
On a cross country flight, just as instrument conditions and night, it's not a matter of "who" gets to log the flight. Everyone logs that time, if acting as a required crewmember. It has nothing to do with assignment (PIC vs. SIC), or manipulation of the controls. It's cross country, period.
