A blur acts as a low-pass filter, removing high-frequency information from the resultant image. If the high-frequency data that was removed is unique enough th

A blur acts as a low-pass filter, removing high-frequency information from the resultant image. If the high-frequency data that was removed is unique enough that it can't be either guessed or recovered then a blur might be just fine. If the high-frequency data is something that can be easily guessed, extrapolated, etc. then a blur does not provide much protection as far as the information content goes.