They wouldn't. I'm going to make the assumption that the passenger being discussed by the OP arrived at the gate after boarding was closed. Otherwise, they would have just boarded along with the other passengers, and the only way it would have come up would have been if the GA had offloaded them prior to that point, such that the BP reader rejected them even though it allowed everyone else in line to continue boarding. If that had been the case, I think it very probable that this would have been mentioned in the OP. Since it wasn't, and also since the flight went out with empty J seats meaning there wasn't the last person on the upgrade waitlist or NRSA to clear, I assume that boarding was closed when they got there and they had to speak to the GA directly.
Not a problem, as long as by "last" you mean immediately after the second-to-last person. They're not going to close the boarding process while people are still boarding, regardless of the time. But, if everyone in the gate area has boarded, and you're not there, and it's less than T-30 for an int'l flight, then you risk being offloaded. The fact that most of the time, boarding doesn't finish until T-20 won't help you if on a particular flight it finishes at T-35, they wait until T-30, and you're not there yet. They may or may not offload you at that point, but it's the risk you take if you're not there at that point.
Also, regarding the checked-bag reason given by the GA, isn't it possible that this is red herring? Perhaps the GA knew that the real reason was that they closed the flight at T-29 as they are entitled to do, and that in their experience, passengers arriving soon after that time are more likely to accept a security-related-sounding explanation regarding checked bags rather than "T-30 is the rule and you're late," which inevitably in a situation such as this leads to further argument and discussion since "it's not my fault I'm late." That is, perhaps there is no rule regarding checked bags not making it, at HKG or anywhere else, even in this particular GA's mind.