The invite to dinner by Jill absolutely depends on your affinity not being DIK
Maybe you are confusing Affinity with Dik status. Dik status only affects dialogues, but your affinity has major affects on paths and branches.
Edit: Also Jill's path is all connected to the picnic. keep affinity to not DIK and everything flows properly to getting the dinner invite.
Choices are go to Picnic, fight for her and go to perp mansion and get the masturbation scene, which finally leads to invite.
Dont see any connection to the DND game to these scenes.