If you are low budg, take the risk, act like you are supposed to be there, but don't be arrogant. If you can afford being shutdown compared to paying for permits, then that's what you do.
Other way is...
Do your research. Federal land is easier to get permits for, and cheaper, compared to state land or private. Talk with the LA Film Commission, they are very helpful. And yes, if you are in public and shoot background, no one can dispute, thus paparazzi.