As far as I can tell, the Rigging section makes no mention of having to have a Control Rig for Rigging.
The Control Rig Cyberware in no way mentions the cyberware being necessary, just that it provides bonuses.
The various archtypes (Drone Rigger, Hacker and Smuggler) all have control rigs, but it could just be that for 10k, the bonus is too much to pass up.
The Matrix Jargon on page 215 suggest that the Control Rig simply enhances the rigger's abilities, not necessarily required. On page 216 the Rigger is defined as "Often equipped with a Control Rig."
And yet, on page 341, where we find out how to adapt a vehicle to a rigger (Rigger Adaptation), we find the following phrase.
QUOTE
Rigger Adaptation: When added to a vehicle, this “black box� allows a character with a control rig (see p. 331) to rig the vehicle
Which suggests that if you want to rig, you, well, need the rig.