The main drive for Gil to face the public I think is the pressure from her company. She is bounded to preform if her boss needed her to. She is not there to proclaim any statement about her past action.
I think reason behind is because of the many advertisement Gil is representing. Her company will face a lot of legal claims if Gil proofs to be unwelcomed due to this incident. This is actually a very cruel punishment to Gil. It is not easy for one to face her family and friends if this happened to an ordinary people not to mention that her image is bread and butter to her living and those she support.
Just a footnote, I'm never a fan of any celebrities.