The reality TV star was stunned to hear the CASANOVA actress is planning to petition British Prime Minister Tony Blair to seek protection laws for celebrities from photographers.
However, Osbourne believes Miller deserves the press attention, because she has regularly discussed her private life with the media.
Osbourne says, "It's what you get - I mean, don't be famous if you don't want it.
"Don't spill your beans to everyone, and don't be famous if you don't want some attention.
"In some ways, I feel sorry for her, because she has had a lot of trouble, but - come on - you choose to be a celebrity, it's part of the job."