I took it to mean that all of the ticketed passengers couldn't be boarded in time for the scheduled take off time.
In so many words, that's correct. But, it leaves unanswered why they didn't board in time.
I believe the passengers don't even know the reason for this particular delay. I was delayed in boarding a few weeks ago, after a cryptic announcement from the gate agent. Under questioning by multiple passengers who knew better, she still wouldn't be specific about the reason.
Since this was in conflict with the airline's earlier promises to keep passengers informed about the duration and reason for delays (under threat of federal regulation), I was surprised and considered filing a complaint, as I'm a regular passenger. But, shortly thereafter I read about the random checks and realized that was the cause.
I decided to not hassle them about it, as I can understand why they wouldn't want to announce it. Some flyers would get worried, because they might think it wasn't truly random.