Rare are the circumstances where I beg to differ with you, but this is one of them, because most other clubs of which you're a member won't have a boarding pass with status printed on it as a requirement for entry. If, as we know, BAEC status can be looked up, it shouldn't really be more than five lines of code to ensure that the status printed on the BP is in fact valid, current and accurate. Why this is only a major issue at T5 is beyond me -- but for whatever reason (two separate wallets mostly) sometimes I just don't have the card with me, and the arrogant attitude and undertones of suspicion of most of those T5 dragons really is, to me, just taking the mick.
BPs can often have the wrong status on them. For instance, if a passenger has forgotten their card and asks us to put the info into their PNR, they will remember the number and then say they're a gold, silver or blue member.
However, I've had situations where the passenger has told me they're gold or silver and I put their number in and the system accepts it and issues a BP accordingly. However, when I've had chance a little later on to check it I discover they're actually a blue member and thus not entitled to lounge access.
Yes, BA's systems should pick this up and automatically revert to the correct status (perhaps Dilly could pass this on to see if it could be done), but at present they don't. Hence lounge agents are continually having to check what correct status is. And when they find out somebody is really a blue member they then have the embarrassing situation of having to tell them their status no longer allows access, etc, etc and this holds up the queue.
In the same way BA systems should show correct status, it would be nice if passengers always told the truth!! Perhaps it's the amount of times agents are not given a true story (numerous times a day, far more than you'd realise) is what makes them suspicious

I do accept there's no reason for them to be arrogant though.