Any diet based on eating fewer calories than you consume will work whether the calories are from fat, carbohydrate or protein, but any diet that excludes any food group altogether is not only unhealthy, but will be impossible to stick to long term.
I wouldn't take any notice of celebrity fad diets, as it's probably quite easy to have (or appear to have) the perfect body if you can afford a personal chef, and spend all day with your personal trainer because you don't have to do a proper job. It also helps that people who make a living out of their looks can afford to have any offending wobbly bits smoothed/removed/lifted by a cosmetic surgeon, and after all that have their photos touched up anyway.
People (well, most people) aren't that stupid to believe everything they read. If an article in Heat magazine claiming Victoria Beckham lives entirely on whelks* has that much of an influence on the eating habits of the nation, why are there so many fat people in Britain?
*I made that up, don't go eating a kilo of whelks to lose weight! (Alternatively, buy the Victoria Beckham Whelk Diet priced �9.99 from all good fishmongers!)