Sure you did. You could have chosen to say no. Luckily for you however, your situation was one where the state considers “OK, I’ll do it” to be an acceptable answer.
I believe it was previously explained that ‘no choice’ in this context basically means ‘no equivalent or better choice’. In the state’s eyes, prostitution > death, so if her only other choice is death, ‘no choice’ is appropriate. (Haven’t read further, but judging by the previous example, her THINKING her only other choice is death would apply too. I do suspect that the threat may have been empty to match the fire in the previous one not being a real danger.)