There isn't nothing wrong with eating greasy food, as long as every meal you have isn't a greasy one; that's when it gets unhealthy.
You can't have a good meal without some fat in it anyway. The body needs fat and puts it to good use. Also fat adds to flavour. No Fat = No Flavour.
If all someone eats is sausage and chips, burgers etc. Then the best thing you can do, to eat healthy, is to cook everythin in the oven. Food cooked in the oven can cook in its own fat; there is no need to add extra, like if you was to shallow fry something.