When Demi Lovato entered rehab she told the world it was because she had an eating disorder. This was despite the fact she had just gone off on a backup dancer with a beat down. Demi admitted later that she had a serious drug and alcohol problem. Of course it did take Demi years to admit that but she finally did. She stuck to that eating disorder story for quite some time.
Ke$ha checked into the same place but I doubt she will be able to stay for months on end like Demi did. It would be great if she could or would but she will feel a ton of pressure from her record label and management to hit the road and support Timber and the new record and make them some money. They will tell her that she can get better after she tours and then they will tell her she can get better after she records another record. It is a vicious cycle and record companies never want to let you off.
When you have the number 2 selling digital single of all time (Tik-Tok) the record company wants you out there and bringing in that gold. I really do hope Ke$ha gets better and listens to herself and the people closest to her.