She's doing it for her mom. The night the incident happened, the media crowded the Taneja's and Leela's upbringing was questioned. If Twinkle had said that Kunj did try to rape her then not only would Kunj have been defamed but also Leela as she was the one who chose him for her and continuously told the world what a great man she has chosen for her daughter. If she had denied the accusation, then her mother's upbringing is questioned as she is a single mother and she might have spoiled her daughter to the point where she has lost her cultural roots.
However, Twinkle didn't exactly answer their questions as she instead questioned who the hell were they to barge into their personal lives. But the media had basically created a situation for Twinkle where no matter what she did, she and Leela would have lost face. So, to protect her and their integrity, she said yes.
I may be wrong as it is quite late right now and I'm not able to think too clearly. Hopefully someone else can shed some better light onto this for you.