Did Kesha lie about being assaulted by Dr. Luke?

Did Kesha lie about being assaulted by Dr. Luke? According to a report by TMZ, they have uncovered a video where in a deposition made in 2011, Kesha flatly denied that she was a sexually assaulted by Dr Luke. However, fast forward to 2016 and she is accusing Dr Ken of drugging and raping her. It is possible that Kesha was afraid to admit to this at the time, after all whe was in the prime of her career and if the incidents did occur, they didn't seem to bother her then.

image Kesha credit Eskimo Jo Wikimedia Commons

The question I have is why not make a formal police report of sexual assault by Dr Ken? Afterll Bill Cosby is before the courts right now for alleged assault that occurred a decade ago. I don't know the answer. Maybe she was raped and drugged maybe she wasn't. The only way to get to the bottom of these allegations is in a court of law dealing with te specific issue and not as a side isse to getting out of a contract.