Everything you were told was correct. Another bill that passed extended reciprocity to any state that does not require a permit to concealed carry. Currently, those states are AZ, AK, WY and VT. A driver's license from any of those states will serve as a handgun license in Oklahoma after Nov 1.
The other you mentioned is not exactly new. The SDA has provided that all persons in a vehicle who are concealed carrying are legal so long as they are not prohibited persons, and one person in the vehicle has a CWL. The only changes from SB1733 to that are it 1) adds unconcealed to concealed, and 2)CWL becomes a "handgun license".