I've read this a few times on the boneyard and well, it's just wrong. All of our 'rivers' are concrete to deal with run off, Certain streets have 18" high curbs to act as run off corridors. There are massive storm drains. There are huge areas for holding storm water. The infrastructure is there.
There is only so much you can do when 1) the soil isn't the type that will hold a lot of moisture and 2) you are surrounded by hundreds of miles of mountains up to 10,000ft tall that all run into LA and 3) you get rain rates of over an inch an hour from the super saturated warm pacific ocean.
We are in fact built to deal with huge rainfalls. But just like you can't build everything in the gulf to survive a direct hit from a cat 5, you can't get enough infrastructure to deal with the really massive storms. And hillsides have been sliding for millions of years - it's in their nature. Back east just dealt with it a long long time ago compared to the west.