I'm pretty sure the airlines that are listed on the chart refer to the airline you are travelling with!
You were travelling with Thai Airways, and it it is clearly indicated that Star Alliance Gold (SAG) will get you into the lounge.
You are right to complain. And I don't believe how stupid these dragons must be to not understand these simple access rules. After all this is the main thing they have to know!
Edit: Just saw the last line in the picture and it says that "SAG of CA, JP, LH, ..., TK, US" have access. BD is missing, and so are SA, OS, UA, FM, JK, KF and SK. Very strange! And definitely against *A rules!