Let me clear this up...
More like a summons. I didn't see the show in question but a past misdemeanor A&B w/o weapon, not domestic, is not an arrestable offense.
IN CALIFORNIA, Battery is arrestable in the past based on PC. Further more, California penal code allows for a citizens arrest. 99% of the time, SDPD would not have booked her, they would have had the complaintant sign the citizens arrest form, then they would have issued her a notice to appear 45 days from the date of incident. The complaintant would then be required to appear in court as well. They arrested her to make an example, and to show for the cameras. I do not object to what they did, but they did have the option to release her with a notice to appear.
Below is the california penal code pertaining to citizens arrest, you will see that it allows for a citizens arrest for just about anything... Additionally, if a private person places someone under citizens arrest, they are authorized to use reasonable force to subdue, and restrain the person until police arrive. At that time, the person gives custody to the PD, and they either book them, or issue a notice to appear. As an interesting side note, California Peace Officers are required by statute to accept any prisoner arrested by a private person. They must either book the suspect, or issue a notice to appear in court.
California Penal Code 837 reads as follows...
837. A private person may arrest another:
1. For a public offense committed or attempted in his presence.
2. When the person arrested has committed a felony, although not
in his presence.
3. When a felony has been in fact committed, and he has reasonable
cause for believing the person arrested to have committed it.
This law also allows for security officers, loss prevention, etc. to make lawful arrests, and then be required to go to court to prove their case.