Is your game version, 0.4.1 and above. I've checked with Regina telling you to solve puzzle and then doing it. Also tried doing the puzzle first and talking to Regina. In both case she did gave me Rachel eventually. Checked code for any issue but there are none. So it's either you are version 4.0.X or you are doing something wrong.
Alright, I was looking at wrong part of the code for any mistakes. Sorry, you are right. The quest is still bugged for anyone who haven't reset the recruits or apartment questlines. The fix should reflect in update 0.4.2. You can wait until then or reset recruits(you will need to get Michelle, Sabrina, Len and others again) to retry the quest. Alternatively you can edit a value in save file but first make a back up of it so you will not lose your savegame. Then in that save file look for "save dataController.saves.secretLoverQuest" and change it's value from 6 to 8.