The BA staff member I spoke to on the telephone (my partner passed him her phone so I could speak to him) was very helpful and explained that it'd be on his head if he got it wrong so he needed to make sure he was correct. He said he didn't work in the lounges very often and that is was quite confusing to know what is and isn't applicable.
Unlike the previous time when the BA staff member was downright rude, on this occasion I felt quite sorry for the BA staff member and think he went out of his way to try and seek clarification. The problem is that he escalated to 2 separate people before speaking to me. The first person said Lounge Access wasn't allowed and the second said that it was!
Disappointing that BA cannot get the basics like this correct. Their staff on the frontline seem to be quite often under-supported in this regard. It's a shame.