Sounds to me like an another surly T5 check-in experience.
Possibly. Then again, sometimes staff come across as "surly", "aggressive" or "arrogant" when they're merely doing the job that British Airways has asked them to do.
We do get a lot of "chancers" trying to get away with using facilities that they are not entitled to use and that does make us appear bullish sometimes. In the present climate, staff are "under the cosh" and are receiving emailed warnings (known as CSIP's) for minor transgressions which, in turn, makes them reluctant to bend rules for anyone no matter how petty and trivial it may appear.
I would suggest that card holders are prepared to produce the card, or their printed boarding pass or itinerary that shows their status, if they wish to use the Zone J facility.