It is true for some cities, not the whole state, YET!

Some cities, most notably San Francisco, Oakland, Berkeley, Santa Monica, West Hollywood, East Palo Alto, have very strict rent control, the rent increase can only be a fraction of consumer price index.  During recent years, the inflation has been low, and 2-3% is typical.  Other cities are not as strict, some have 5% cap, others may not have rent control yet.  But there is new Prop 10 on the November ballot that would allow rent control on single family house, condos, and townhomes, and newer building, which were previously excluded from rent control by a state law.  This is a bad idea and would hurt everyone in the end.  So, if you live in California, please study this new Prop 10 carefully and make informed decision.  There are many academic studies on rent control, most economic experts agree that rent control is bad because it depletes limited supply and therefore drives the rent even higher.  Both San Francisco Chronicles and San Jose Mercury editorial board oppose prop 10: 

https://www.sfchronicle.com/opinion/editorials/article/Chronicle-Recommends-No-on-Prop-10-13231228.php

https://www.mercurynews.com/2018/08/25/editorial-prop-10-would-exacerbate-californias-housing-crisis/

https://www.forbes.com/sites/wlf/2018/08/20/wake-up-california-millennials-rent-control-is-a-generational-con-game/#9060e5d397b8