Although ICBC is the one paying the bills on most claims, they are not necessarily the entity you are naming as a Defendant in a lawsuit.
If you are a passenger in a vehicle driven by one party, which strikes another vehicle, depending on who is at fault, you may pursue your personal injury claim against one or both of the drivers involved in the accident. ICBC simply steps in and appoints its own defense counsel to defend the claim.
If you are a driver of a vehicle and you were injured as a result of the actions of another party, you will be pursuing the driver(s) and owner(s) of the at-fault vehicle(s) involved in the accident. However, ICBC is directly sued in a lawsuit if you are trying to pursue Part VII/No-fault benefits (i.e. disability and medical expense benefits) and ICBC is denying payment.