In general yes, but I think Prop 13 complicates matters, because it's not just a lower tax rate, but rather applies unequally to different properties based on their transaction history. (e.g. a property built or sold recently gets high taxes, while one that's been unchanged remains low)
So we can divide the rental market into high-tax and low-tax properties. The landlords of high-tax properties must incorporate the tax into the rent. Meanwhile, the landlords of low-tax properties can set their rents just as high, since they compete in the same market, and pocket the tax difference.
In contrast, a flat property tax reduction would increase the profit margins of all landlords equally, and any one of them could start undercutting the others and be undercut in return, which over time in an efficient market will tend to lower prices back to a similar margin before the tax reduction.
So we can divide the rental market into high-tax and low-tax properties. The landlords of high-tax properties must incorporate the tax into the rent. Meanwhile, the landlords of low-tax properties can set their rents just as high, since they compete in the same market, and pocket the tax difference.
In contrast, a flat property tax reduction would increase the profit margins of all landlords equally, and any one of them could start undercutting the others and be undercut in return, which over time in an efficient market will tend to lower prices back to a similar margin before the tax reduction.