Joyner seems mostly right, but I believe the $70M figure he is using is the luxury tax level, not the salary cap.
The salary cap for the current season is just north of $58M.
The Spurs can exceed this number to sign their own free agents. They can't exceed it sign other free agents.
They can also exceed the luxury tax number for their own guys. Each has a cap hold until signed or renounced, so they will not be below the salary cap at all.