I did some online research into San Fransiscos municipal codes (I assume by "the Bay area" that you mean SF). While I found a few specific knife laws for SF, none of those laws mentioned carrying knives in ones vehicle. And unless the law specifically forbids doing something, then it isn't illegal.
What they did say is- It is illegal to "loiter", or get into a fight, while carrying conceald any knife with a blade 3 inches or longer. And while "loiter" is a rather loose term, the law specifically provides an exception for people carrying a knife for normal use as a tool.
It is illegal to sell, transfer, or otherwise give a knife to a minor. There are exceptions to this, like a parent taking their child camping or giving a child a knife for use with food.
Switchblades are illegal. And since they didn't specify the size of the blade, I will assume that all switchblades are illegal. As opposed to CA state law that permits the carrying of a switchblade with a blade under 2 inches.
Personally, after what I've read (and didn't read) I wouldn't be at all concerned about carrying knives in the drivers compartment of a car.
And I wouldn't ask any law enforcement personnel (cops, DA's) about such matters, after all, people working in such professions tend to have a strong prejudice against people carrying knives in any manner. Like you suggest, they could easily just tell you what they want you to think and do. No offense meant to people in those professions, I just think that's the way it tends to be.
But as always, when in doubt, consult a local defense attorney.