In my opinion if you cannot go more than a day without your hair getting greasy you are washing it wrong!
It's nobodies fault, most of us were never taught how to do it correctly. Once I figured out how to wash properly and which products I should be using for my hair type, I could go up to a week and half without washing my hair depending on my activities through the week.
So can you go more than a day without your hair getting greasy?