It's the same as how a burglar "can't" rob your house. Of course they can, and then you get to attempt legal recourse afterward, which sometimes works.
Especially given that the officers were told by higher-ups, you wouldn't want to press criminal charges against the individual officer anyways - you'd be better off with a civil suit against LAPD.
Legal recourse? I suppose people could maybe bring civil suits against burglars, but generally they face criminal charges, and you make an insurance claim?