Rather than complaining about the staff, OP should have read the clear and concise rules. He was not entitled to access. I can't think of a worse idea than having staff spend their days making calls to obtain exceptions. Everybody thinks that they are special. Nobody is.
The language is clear and OP had a perfectly good alternative.
These [Arrivals] lounges are exclusive to you if you have travelled in First or Club World, or are a Gold Executive Club Member, arriving on a British Airways longhaul flight.