From JAR-FCL1:
(c) 20 hours of cross-country flight as pilot-in-command including a VFR cross-country flight totalling at least 540 km (300 NM) in the course of which full stop landings at two different aerodromes from the aerodrome of departure shall be made;
From ICAO Annex 1:
b) 20 hours of cross-country flight time as pilot-incommand including a cross-country flight totalling not less than 540 km (300 NM) in the course of which full-stop landings at two different aerodromes shall be made;
provided you hold a licence that entitles you to carry passengers, then there is nothing to prevent it!
I think the requirement is perfectly clear. You say that the FAA require you to do it SOLO but thats not what my copy of FARS states!