I will copy and paste some of it below which I really love and agree with:
To maintain healthy hair, Dr. Draelos recommends people also follow these tips:
1. Wash oily hair more frequently. How often you wash your hair should be based on how much oil your scalp produces.
o If your scalp is oily, you may need to wash it as often as once a day.
o If you have chemically-treated hair, your hair may be drier, so you may want to wash it less frequently.
o As you get older, your scalp makes less oil, so you may not need to shampoo as often. But if you see flakes in your hair, you may not be shampooing enough. This can lead to dandruff and other scalp diseases.
Sorry I know its been a while since this was posted but I came across this looking for hair growth tips. Its suggested that an oily scalp should be washed more often, but its the oil good for you. Following the same logic as over washing oily skin, overwashing oil hair might strip it of its natural oils.
I think the point is the more oily it is the greater the amount of natural skin oil AND grease. Greasy scalp or skin is never really a good thing and works to trap bacteria causing inflammation, you never want that.
If you are getting flakes of your hair, you are not shampooing enough?! Your scalp starts flaking when certain shampoos dry the hell out of your scalp.
TBH I have experience with the reverse being true also but I think it greatly depends on the kind of shampoo you are using