http://www.dmv.ca.gov/pubs/vctop/d11/vc22348.htm
"(c) A vehicle subject to Section 22406 shall be driven in a lane designated pursuant to Section 21655, or if a lane has not been so designated, in the right-hand lane for traffic or as close as practicable to the right-hand edge or curb. When overtaking and passing another vehicle proceeding in the same direction, the driver shall use either the designated lane, the lane to the immediate left of the right-hand lane, or the right-hand lane for traffic as permitted under this code. If, however, specific lane or lanes have not been designated on a divided highway having four or more clearly marked lanes for traffic in one direction, a vehicle may also be driven in the lane to the immediate left of the right-hand lane, unless otherwise prohibited under this code. This subdivision does not apply to a driver who is preparing for a left- or right-hand turn or who is in the process of entering into or exiting from a highway or to a driver who is required necessarily to drive in a lane other than the right-hand lane to continue on his or her intended route."
http://www.dmv.ca.gov/pubs/hdbk/traffic_lanes.htm
Choosing A Lane
Traffic lanes are often referred to by number. The left or
"fast" lane is called the "Number 1 Lane." The lane to the right of the "Number 1 Lane" is called the "Number 2 Lane," then the "Number 3 Lane,
Drive in the lane with the smoothest flow of traffic. If you can choose among three lanes, pick the middle lane for the smoothest driving. To drive faster, pass, or turn left, use the left lane. When you choose to drive slowly or enter or turn off the road, use the right lane.
If there are only two lanes in your direction, pick the right lane for the smoothest driving.
Do not weave in and out of traffic. Stay in one lane as much as possible. "
"Passing Lanes
Before you pass, look ahead for road conditions and traffic that may cause other vehicles to move into your lane.
Never drive off the paved or maintraveled portion of the road or on the shoulder to pass. The edge of the main-traveled portion of the road may have a painted white line on the road’s surface. Passing other vehicles at crossroads, railroad crossings, and shopping center entrances is dangerous.
Pass traffic on the left. You may pass on the right only when:
* An open highway is clearly marked for two or more lanes of travel in your direction.
* The driver ahead of you is turning left and you do not drive off the roadway to pass. Never pass on the left, if the driver is signaling a left turn."
http://www.dmv.ca.gov/pubs/curriculum/Unit%207.pdf
"The right-hand lane(s) on a freeway is (are) for slower moving
traffic and leftmost lane(s) is (are) for faster traffic. Move to a
slower lane if a vehicle is following closely behind you, even
if you are obeying the speed limit. Left lanes should be used
for passing slower moving vehicles"
So...it appears that to a point, we're both right.
BUT, in no case, is it legal to drive faster than the posted limit in the "fast lane."