That is technically true, but not really true. The basic tax rate is indeed 1%, but counties and cities are free to add any kind of fees they want (AFAIK there is no limit) to your property tax so in practice you're paying way more than 1% in CA.
Irvine CA wanted property tax and so they get builders to force you to an extra fee but it isn't technically a property tax.
Not to say there isn't sometimes a fee or two added but it isn't the Wild West at all.
That is the loophole they use. They add all kinds of fees into the property tax but don't classify them as taxes. Best I know, there is no limit to how many and how much. Twenty years ago my property tax was just a single line item, the property tax. Now it's up to 6-7 (don't have the bill in front of me to check exact count) line items.
So yes, your CA propery tax^H^H^Hfee bill can be way over 1%
If you can't afford less than $1k per month you could just sell your $1 million house.
Those numbers aren't being dramatic. You need a $1.2 million house to pay $1k a month in property taxes.