My son also had an oily hair problem. We too, found out it was from lack of using SHAMPOO! We narrowed it down to....
1) He was not using shampoo...just lazy and did not want to wash it. Wetting was easier.
2) He was using shampoo, but not ALL OVER.....you know when this happens because the hair on the top would be clean, but the sides and bottom would be still greasy.......again....laziness!
3) He was using shampoo, but possibly holding it under the shower stream and the stream would cause the shampoo to rinse out of his hand before getting to his head.
ETA: Also, make sure she is getting the shampoo to her scalp. If the shampoo is not getting to the scalp, the greasy look is always going to be there. Sometimes with long hair, a child concentrates only on making sure the lather gets on all the ends. Honestly, I would think no matter how greasy a persons hair/scalp tends to be, that first hour or so after washing and drying, the hair should look clean.
Hope this helps.