From my reading in the press, identity thieves tend to go for bigger windfalls than purses. Think about it, if someone is going to go to the trouble of stealing your identity and obtaining credit cards in your name is "a purse" really going to be high on their list of priorities? I think not.
Furthermore, ...if they're going to steal your identity, why would they bother with stealing a rental purse, when they can simply use your forged credentials to buy the real thing?
Services like this are for posers.