How can the GSW's offer less than any other team? That doesn't make sense; can anyone explain this to me???
It's not that the Warriors can offer less than any other team, it's that they can offer less than a team that's under the cap. You're allowed to go over your cap in order to max out a former first-round draft pick -- but not a second-rounder, which is what Arenas was. So Arenas is completely up for grabs, and the Warriors can offer up to their median exception, same as almost everybody else.
The few teams that have lots of room under the cap (San Antonio, Denver, L.A. Clippers, maybe Utah) can offer Arenas as much as they want.