I couldn't see any fringing on the petals (but it could have been still developing) and they were very deep blue purple even for Thysanotus tuberosus. Also the stems seemed to be twisting around the other plants.
Have a look at other photos of Thysanotus patersonii on this site. They have a different growth habit - the stems are very bent and curly. The stems here are all straight, like Thysanotus tuberosus. The colour of the flower is can vary.