That is not a fair assessment of the situation. There are a number of factors that have been put in place by the populace and government agencies to force this situation in the bay area:
1. Rent Control: This forces an incentive not to move. If you are in the 4-bedroom house at $1,500 a month for the past 15 years, a comparable 4-bedroom house is now $6,000. There is no incentive to move and owner's have little incentive to bring up to standard something they are not going to get an ROI on. In this instance, Prop 13 actually makes the situation bearable for the landlords, think if the costs went up and your return stayed static.
2. Building Restrictions: Between the historical board, local populace anger to building, and zoning enforcement, the bay area's supply has been static while demand has increased. There are workarounds, but they border on illegal (i.e. the guy who turned a storage closet into a baby's room for additional space); essentially sub-dividing up existing property.
Within the Bay area, the ability to move a demand curve down has not existed, so the prices have risen to meet the existing supply. Prop 13 has no direct effect on these two items except a positive effect for the landowners in reducing the tax burden that would have forced early bankruptcy for them because of the rent control.