False.
Initial reports suggested the Guardsmen were unarmed. However, Border Patrol spokesman Gustavo Soto said the teams "had rifles and ammunition from Day One."
Mixed Reports on National Guard Border Confrontation
http://www.foxnews.com/story/2007/02/01/mixed-reports-on-national-guard-border-confrontation/
February 01, 2007
Not all NG were armed; it depended on the assignment. Building roads and fences, not armed. Entry Identification Team, armed.
In my area NG were armed, on patrol and spotting for BP in remote areas on the border, with no ammo and were also told no contact with illegals. In fact they were told if illegals came toward them they were to leave the area. I know that for a fact. At the time due to my employment situation I could not say that in public but it was absolutely true.