Earlier quoted context omitted.
Imagine the bike lane is on the right. Now if cars are moving slowly you as a cyclist will be passing them on their right ("undertaking"). This is unsafe near the places where cars turn right (across the bike lane).
In California: 1. A bicyclist does not need to stay to the right of the road when approaching a place where right turns are allowed (i.e. can leave the bike lane). 2. Vehicles are required to merge into the bike lane before making a right turn, otherwise it's consider making a turn without being in the rightmost lane. Not to say I've ever seen a single car in the bay area correctly merge to the bike lane before turni…
If you're just worried about cars, it's fairly safe to make the right turn lane from that non-rightmost lane, since the other car is blocking any other car from approaching there. However, bikes (and sometimes motorcyclists, but rarely are they that suicidal) are going to come up, so it's still prudent to both get into the far-right lane and check on the right. That's the most common "cars turning right from non-rightmost lane" situation I've seen, though.
My biggest question about California road rules: what kind of vehicle is a homeless guy with a shopping car full of cans/etc.? Is he a pedestrian (similar to a pedestrian pushing a stroller), or is he a vehicle like a bicycle? What if he's in a lane of traffic, going down the road at 1-2mph (which is reasonable, since he would take up the entire sidewalk otherwise).