Wait... So Harley Quinn confessed to killing Jason Todd? Well, according to her rap-sheet she did.
Now, that's no indication that she did kill Todd, it just means she confessed (which she could have done to protect her love), BUT it ruins the Joker's mythology. He killed Jason as a statement, to really f*ck with the Bat, and him being haunted by not being able to save his sidekick was a pretty key development in the Joker/Batman dynamic.
Publicly surrendering that to Harley Quinn is just not right. It might further express her transformation, but it's an empty, showy sentiment. The Joker's power over Harley is already over-stated by her voluntarily leaping into the ACE vat, rather than him throwing her cruelly. Having her then copping to this is just over-egging it and taking away from the Joker.