Thanks for all the advice. As I placed in my original post, I knew what the stated summary rule was, but wondered whether there was an unpublished official exception that someone might have experienced. Apparently not.

I'll nevertheless give it a shot as the SQ lounge, although not one of SQ/s best, is nevertheless better than the LH Senator lounge, which I can get into with a family member (or any guest).

I am not on a Star Alliance flight, so there is no means of gaining entry into any of the TG lounges, which are now quite nice in light of the renovations over the past year or two.