The press tends to lump in everyone assigned to an SF unit as "Green Berets". While support personnel are vital to the completion of the mission, they are not "Green Berets", even though they are assigned to an SF unit.
Unless things have changed, the only ones authorized to wear the green beret are men who have completed the Special Forces Qualification Course, commonly referred to as the Q Course.
During my time, it was 12 SF guys to a team, if you had a full team, which was very rare. 6 teams to a company, plus company HQ, so less than 100 per company. So even if an entire Battalion was used, it would still be less than 400 actual SF qualified guys on the ground.
Once again, it's probably shoddy research on the part of the reporter.
Of course. What should I expect from the cutting edge media types.